{"id":4526,"date":"2016-05-16T11:49:00","date_gmt":"2016-05-16T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/"},"modified":"2018-05-08T16:55:54","modified_gmt":"2018-05-08T11:25:54","slug":"ncert-solutions-class-12-maths-exercise-10-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 10.2"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#NCERT_Solutions_class_12_Maths_Vector_Algebra\" >NCERT Solutions class 12 Maths Vector Algebra<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#2_Write_two_different_vectors_having_same_magnitude\" >2. Write two different vectors having same magnitude.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#3_Write_two_different_vectors_having_same_direction\" >3. Write two different vectors having same direction.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#4_Find_the_values_of_and_so_that_the_vectors_and_are_equal\" >4. Find the values of \u00a0and \u00a0so that the vectors \u00a0and \u00a0are equal.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#5_Find_the_scalar_and_vector_components_of_the_vector_with_initial_point_2_1_and_terminal_point\" >5. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#6_Find_the_sum_of_the_vectors_and\" >6. Find the sum of the vectors: \u00a0\u00a0and \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#7_Find_the_unit_vector_in_the_direction_of_the_vector\" >7. Find the unit vector in the direction of the vector \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#9_For_given_vectors_and_find_the_unit_vector_in_the_direction_of\" >9. For given vectors \u00a0and \u00a0find the unit vector in the direction of \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#10_Find_the_vector_in_the_direction_of_vector_which_has_magnitude_8_units\" >10. Find the vector in the direction of vector \u00a0which has magnitude 8 units.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#11_Show_that_the_vectors_and_are_collinear\" >11. Show that the vectors \u00a0and \u00a0are collinear.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#12_Find_the_direction_cosines_of_the_vector\" >12. Find the direction cosines of the vector \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#13_Find_the_direction_cosines_of_the_vector_joining_the_points_A_and_B_directed_from_A_to_B\" >13. Find the direction cosines of the vector joining the points A\u00a0and B\u00a0directed from A to B.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#14_Show_that_the_vector_is_equally_inclined_to_the_axes_OX_OY_and_OZ\" >14. Show that the vector \u00a0is equally inclined to the axes OX, OY and OZ.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#15_Find_the_position_vector_of_a_point_R_which_divides_the_line_joining_two_points_P_and_Q_whose_position_vectors_are_and_respectively_in_the_ratio_2_1_i_internally_ii_externally\" >15. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are \u00a0and \u00a0respectively, in the ratio 2 : 1 (i) internally (ii) externally.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#NCERT_Solutions_class_12_Maths_Exercise_102\" >NCERT Solutions class 12 Maths Exercise 10.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#16_Find_the_position_vector_of_the_mid-point_of_the_vector_joining_the_points_P_2_3_4_and_Q\" >16. Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#NCERT_Solutions_class_12_Maths_Exercise_102-2\" >NCERT Solutions class 12 Maths Exercise 10.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#17_Show_that_the_points_A_B_and_C_with_position_vectors_and_respectively_form_the_vertices_of_a_right_angled_triangle\" >17. Show that the points A, B and C with position vectors \u00a0and \u00a0respectively form the vertices of a right angled triangle.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#NCERT_Solutions_class_12_Maths_Exercise_102-3\" >NCERT Solutions class 12 Maths Exercise 10.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#18_In_triangle_ABC_Fig_below_which_of_the_following_is_not_true\" >18. In triangle ABC (Fig. below), which of the following is not true:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#NCERT_Solutions_class_12_Maths_Exercise_102-4\" >NCERT Solutions class 12 Maths Exercise 10.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#19_If_and_are_two_collinear_vectors_then_which_of_the_following_are_incorrect\" >19. If \u00a0and \u00a0are two collinear vectors, then which of the following are incorrect:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#NCERT_Solutions_class_12_Maths_Exercise_102-5\" >NCERT Solutions class 12 Maths Exercise 10.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 10.2 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p><strong>Download\u00a0<a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics-vector-algebra\/1294\/ncert-solutions\/5\/\">NCERT solutions for\u00a0Vector Algebra\u00a0<\/a>as PDF.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/12%20Maths%20Book%20Part-02%20.jpg\" alt=\"NCERT Solutions class 12 Maths Exercise 10.2\" width=\"202\" height=\"259\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Vector_Algebra\"><\/span>NCERT Solutions class 12 Maths Vector Algebra<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\"><strong>1. Compute the magnitude of the following vectors:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 44px; width: 357px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image001.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image002.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 33px; width: 228px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 27px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image005.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 33px; width: 252px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\">Also <img decoding=\"async\" style=\"height: 44px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 56px; width: 383px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image008.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_Write_two_different_vectors_having_same_magnitude\"><\/span><strong>2. Write two different vectors having same magnitude.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image002.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\">Clearly, <img decoding=\"async\" style=\"height: 25px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image010.png\" \/>\u00a0[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image011.png\" \/>\u00a0Coefficients of <img decoding=\"async\" style=\"height: 24px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image012.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image013.png\" \/>\u00a0are same in vectors <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image015.png\" \/>\u00a0coefficients of <img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image016.png\" \/>\u00a0in <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image015.png\" \/>\u00a0are unequal as <img decoding=\"async\" style=\"height: 19px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image017.png\" \/>\u00a0]\n<p style=\"text-align: justify;\">But <img decoding=\"async\" style=\"height: 33px; width: 228px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 33px; width: 227px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image018.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Write_two_different_vectors_having_same_direction\"><\/span><strong>3. Write two different vectors having same direction.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let <img decoding=\"async\" style=\"height: 27px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image019.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 35px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 23px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image021.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image022.png\" \/>\u00a0where <img decoding=\"async\" style=\"height: 15px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image023.png\" \/>\u00a0= 2 &gt; 0<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0Vectors <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image015.png\" \/>\u00a0have the same direction.<\/p>\n<p style=\"text-align: justify;\">But <img decoding=\"async\" style=\"height: 35px; width: 223px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image024.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Find_the_values_of_and_so_that_the_vectors_and_are_equal\"><\/span><strong>4. Find the values of <\/strong><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image025.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image026.png\" \/><strong>\u00a0so that the vectors <\/strong><img decoding=\"async\" style=\"height: 27px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image027.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image028.png\" \/><strong>\u00a0are equal.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 27px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\">Comparing coefficients of <img decoding=\"async\" style=\"height: 24px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image012.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image013.png\" \/>\u00a0on both sides, we have,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image030.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image031.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_Find_the_scalar_and_vector_components_of_the_vector_with_initial_point_2_1_and_terminal_point\"><\/span><strong>5. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point <\/strong><img decoding=\"async\" style=\"height: 27px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image032.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0be the vector with initial point A (2, 1) and terminal point B<img decoding=\"async\" style=\"height: 27px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image032.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image034.png\" \/>\u00a0Position vector of point A is (2, 1) = <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image035.png\" \/>\u00a0and position vector of point B is <img decoding=\"async\" style=\"height: 27px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image036.png\" \/>\u00a0=\u00a0 <img decoding=\"async\" style=\"height: 27px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0= Position vector of point B \u2013 Position vector of point A<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 35px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image039.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image034.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image040.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0Scalar components of the vectors <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0are coefficients of <img decoding=\"async\" style=\"height: 24px; width: 11px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image012.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image013.png\" \/>\u00a0in <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0i.e., <img decoding=\"async\" style=\"height: 19px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image041.png\" \/>\u00a0and 6 and vector components of the vector <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0are <img decoding=\"async\" style=\"height: 24px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image042.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image043.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_Find_the_sum_of_the_vectors_and\"><\/span><strong>6. Find the sum of the vectors: <\/strong><img decoding=\"async\" style=\"height: 27px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image044.png\" \/><strong>\u00a0<\/strong><img decoding=\"async\" style=\"height: 27px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image045.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image046.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 27px; width: 212px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image047.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image046.png\" \/><\/p>\n<p style=\"text-align: justify;\">Adding, <img decoding=\"async\" style=\"height: 27px; width: 299px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image048.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image049.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Find_the_unit_vector_in_the_direction_of_the_vector\"><\/span><strong>7. Find the unit vector in the direction of the vector <\/strong><img decoding=\"async\" style=\"height: 27px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image050.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We know that a unit vector in the direction of the vector <img decoding=\"async\" style=\"height: 27px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image051.png\" \/>\u00a0is<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 56px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image052.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image034.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 48px; width: 229px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image053.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>8. Find the unit vector in the direction of the vector <\/strong><img decoding=\"async\" style=\"height: 25px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image054.png\" \/><strong>\u00a0where P and Q are the points (1, 2, 3) and (4, 5, 6) respectively.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>\u00a0Given: Points P (1, 2, 3) and Q (4, 5, 6)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0Position vector of point P = <img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image055.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image056.png\" \/>\u00a0and position vector of Q = <img decoding=\"async\" style=\"height: 25px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image057.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image058.png\" \/>, where O is the origin.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image054.png\" \/>\u00a0= Position vector of Q \u2013 Position vector of P = <img decoding=\"async\" style=\"height: 25px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image057.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 11px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image059.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image055.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image058.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 11px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image059.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image060.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image061.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, the unit vector in the direction of vector <img decoding=\"async\" style=\"height: 25px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image054.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 56px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image062.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 48px; width: 259px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image063.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 55px; width: 295px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image064.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_For_given_vectors_and_find_the_unit_vector_in_the_direction_of\"><\/span><strong>9. For given vectors <\/strong><img decoding=\"async\" style=\"height: 27px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image065.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image066.png\" \/><strong>\u00a0find the unit vector in the direction of <\/strong><img decoding=\"async\" style=\"height: 23px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image067.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: Vectors <img decoding=\"async\" style=\"height: 27px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image065.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image068.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image069.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image070.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image034.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 48px; width: 256px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image071.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_Find_the_vector_in_the_direction_of_vector_which_has_magnitude_8_units\"><\/span><strong>10. Find the vector in the direction of vector <\/strong><img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image072.png\" \/><strong>\u00a0which has magnitude 8 units.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let <img decoding=\"async\" style=\"height: 27px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image073.png\" \/><\/p>\n<p style=\"text-align: justify;\">A vector in the direction of vector <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/>\u00a0which has magnitude 8 units = <img decoding=\"async\" style=\"height: 24px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image074.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 63px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image075.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 44px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image076.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image077.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11_Show_that_the_vectors_and_are_collinear\"><\/span><strong>11. Show that the vectors <\/strong><img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image078.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image079.png\" \/><strong>\u00a0are collinear.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let <img decoding=\"async\" style=\"height: 27px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image080.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image081.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 35px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image082.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 23px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image083.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image034.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image084.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image085.png\" \/>\u00a0where <img decoding=\"async\" style=\"height: 19px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image086.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_Find_the_direction_cosines_of_the_vector\"><\/span><strong>12. Find the direction cosines of the vector <\/strong><img decoding=\"async\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image087.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>The given vector is <img decoding=\"async\" style=\"height: 32px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image088.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image089.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 48px; width: 315px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image090.png\" \/><\/p>\n<p style=\"text-align: justify;\">We know that the direction cosines of a vector <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/>\u00a0are coefficients of <img decoding=\"async\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image091.png\" \/>\u00a0in <img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image089.png\" \/>\u00a0i.e., <img decoding=\"async\" style=\"height: 44px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image092.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_Find_the_direction_cosines_of_the_vector_joining_the_points_A_and_B_directed_from_A_to_B\"><\/span><strong>13. Find the direction cosines of the vector joining the points A<\/strong><img decoding=\"async\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image093.png\" \/><strong>\u00a0and B<\/strong><img decoding=\"async\" style=\"height: 27px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image094.png\" \/><strong>\u00a0directed from A to B.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: Points A<img decoding=\"async\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image093.png\" \/> and B<img decoding=\"async\" style=\"height: 27px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image094.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0Position vector of point A = <img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image095.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image096.png\" \/><\/p>\n<p style=\"text-align: justify;\">And Position vector of point B = <img decoding=\"async\" style=\"height: 23px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image097.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image098.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0Vector <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 23px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image097.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 11px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image059.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image095.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image098.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 11px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image059.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image099.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image100.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 36px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image101.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 24px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image102.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0A unit vector along <img decoding=\"async\" style=\"height: 56px; width: 173px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image103.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 219px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image104.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, the direction cosines of vector <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image105.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"14_Show_that_the_vector_is_equally_inclined_to_the_axes_OX_OY_and_OZ\"><\/span><strong>14. Show that the vector <\/strong><img decoding=\"async\" style=\"height: 27px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image106.png\" \/><strong>\u00a0is equally inclined to the axes OX, OY and OZ.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image002.png\" \/><\/p>\n<p style=\"text-align: justify;\">Let us find angle <img decoding=\"async\" style=\"height: 24px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image107.png\" \/>\u00a0(say) between vector <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/>\u00a0and OX <img decoding=\"async\" style=\"height: 35px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image108.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image034.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 57px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image109.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 64px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image110.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 47px; width: 164px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image111.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image034.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 44px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image112.png\" \/><\/p>\n<p style=\"text-align: justify;\">Similarly angle <img decoding=\"async\" style=\"height: 24px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image113.png\" \/>\u00a0(say) between vector <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/>\u00a0and OY <img decoding=\"async\" style=\"height: 35px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image114.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image115.png\" \/><\/p>\n<p style=\"text-align: justify;\">And angle <img decoding=\"async\" style=\"height: 24px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image116.png\" \/>\u00a0(say) between vector <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/>\u00a0and OZ <img decoding=\"async\" style=\"height: 35px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image117.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image115.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 24px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image107.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 24px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image113.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 24px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image116.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0Vector <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image002.png\" \/>\u00a0is equally inclined to OX, OY and OZ.<\/p>\n<hr \/>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"15_Find_the_position_vector_of_a_point_R_which_divides_the_line_joining_two_points_P_and_Q_whose_position_vectors_are_and_respectively_in_the_ratio_2_1_i_internally_ii_externally\"><\/span><strong>15. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are <\/strong><img decoding=\"async\" style=\"height: 27px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image118.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image119.png\" \/><strong>\u00a0respectively, in the ratio 2 : 1 (i) internally (ii) externally.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Position vector of P is <img decoding=\"async\" style=\"height: 27px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image120.png\" \/>\u00a0and Position vector of Q is <img decoding=\"async\" style=\"height: 27px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image121.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> Position vector of point R dividing PQ internally (i.e., R lies within the segment PQ) in the ratio 2 : 1 = <img decoding=\"async\" style=\"height: 15px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image122.png\" \/>\u00a0= PR : QR is <img decoding=\"async\" style=\"height: 45px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image123.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 52px; width: 335px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image124.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 184px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image125.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Position vector of point R dividing PQ externally (i.e., R lies outside the segment PQ and to the right of point Q because ratio 2 : 1 &gt; 1 i.e., PR : QR = 2 : 1) is <img decoding=\"async\" style=\"height: 45px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image126.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 52px; width: 347px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image127.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 24px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image128.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_102\"><\/span>NCERT Solutions class 12 Maths Exercise 10.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"16_Find_the_position_vector_of_the_mid-point_of_the_vector_joining_the_points_P_2_3_4_and_Q\"><\/span><strong>16. Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q<\/strong><img decoding=\"async\" style=\"height: 27px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image129.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: Point P (2, 3, 4) and Q<img decoding=\"async\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image130.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image003.png\" \/>\u00a0Position vector of point P is <img decoding=\"async\" style=\"height: 27px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image131.png\" \/><\/p>\n<p style=\"text-align: justify;\">And Position vector of point Q is <img decoding=\"async\" style=\"height: 27px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image132.png\" \/><\/p>\n<p style=\"text-align: justify;\">And Position vector of mid-point R of PQ is <img decoding=\"async\" style=\"height: 41px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image133.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image134.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 45px; width: 163px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image135.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_102-2\"><\/span>NCERT Solutions class 12 Maths Exercise 10.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"17_Show_that_the_points_A_B_and_C_with_position_vectors_and_respectively_form_the_vertices_of_a_right_angled_triangle\"><\/span><strong>17. Show that the points A, B and C with position vectors <\/strong><img decoding=\"async\" style=\"height: 27px; width: 189px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image136.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image137.png\" \/><strong>\u00a0respectively form the vertices of a right angled triangle.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: Position vector of point A is <img decoding=\"async\" style=\"height: 27px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image138.png\" \/><\/p>\n<p style=\"text-align: justify;\">Position vector of point B is <img decoding=\"async\" style=\"height: 27px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image139.png\" \/>\u00a0and<\/p>\n<p style=\"text-align: justify;\">Position vector of point C is <img decoding=\"async\" style=\"height: 27px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image140.png\" \/>\u00a0where O is the origin.<\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0= Position vector of point B \u2013 Position vector of point A<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 35px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image141.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image142.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image143.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 23px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image144.png\" \/>\u00a0= Position vector of point C \u2013 Position vector of point B<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 35px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image145.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image146.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image147.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 23px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image148.png\" \/>\u00a0= Position vector of point C \u2013 Position vector of point A<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 35px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image149.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image150.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image151.png\" \/>\u00a0\u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\">Adding eq. (i) and (ii),<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image033.png\" \/>\u00a0+ <img decoding=\"async\" style=\"height: 23px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image144.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image143.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image147.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image151.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 23px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image148.png\" \/>[By eq. (iii)]\n<p style=\"text-align: justify;\">Now From eq. (i),AB = <img decoding=\"async\" style=\"height: 32px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image152.png\" \/><\/p>\n<p style=\"text-align: justify;\">From eq. (ii),BC = <img decoding=\"async\" style=\"height: 32px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image153.png\" \/><\/p>\n<p style=\"text-align: justify;\">From eq. (iii),AC = <img decoding=\"async\" style=\"height: 32px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image154.png\" \/><\/p>\n<p style=\"text-align: justify;\">Here, we can observe that (Longest side BC)<sup>2<\/sup> = <img decoding=\"async\" style=\"height: 36px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image155.png\" \/>\u00a0AB<sup>2<\/sup> + AC<sup>2<\/sup><\/p>\n<p style=\"text-align: justify;\">Therefore, A B, C are the vertices of a right angled triangle.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_102-3\"><\/span>NCERT Solutions class 12 Maths Exercise 10.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"18_In_triangle_ABC_Fig_below_which_of_the_following_is_not_true\"><\/span><strong>18. In triangle ABC (Fig. below), which of the following is not true:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 5\" style=\"height: 66px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image156.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(A) <\/strong><img decoding=\"async\" style=\"height: 23px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image157.png\" \/><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <\/strong><img decoding=\"async\" style=\"height: 23px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image158.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <\/strong><img decoding=\"async\" style=\"height: 23px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image159.png\" \/><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We know by Triangle law of Addition of vectors that <img decoding=\"async\" style=\"height: 23px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image160.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image034.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image161.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image034.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 23px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image157.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore option (C) is not true because in option (C),<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 23px; width: 243px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image162.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_102-4\"><\/span>NCERT Solutions class 12 Maths Exercise 10.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"19_If_and_are_two_collinear_vectors_then_which_of_the_following_are_incorrect\"><\/span><strong>19. If <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image015.png\" \/><strong>\u00a0are two collinear vectors, then which of the following are incorrect:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>(A) <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image015.png\" \/><strong>\u00a0= <\/strong><img decoding=\"async\" style=\"height: 25px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image163.png\" \/><strong>\u00a0for some scalar <\/strong><img decoding=\"async\" style=\"height: 19px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image164.png\" \/><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <\/strong><img decoding=\"async\" style=\"height: 23px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image165.png\" \/><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) The respective components of <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image015.png\" \/><strong>\u00a0are proportional.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) Both the vectors <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image014.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image015.png\" \/><strong>\u00a0have same direction, but different magnitudes.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Option (D) is not true because two collinear vectors can have different directions and also different magnitudes.<\/p>\n<p style=\"text-align: justify;\">The option (A) and option (C) are true by definition of collinear vectors.<\/p>\n<p style=\"text-align: justify;\">Option (B) is a particular case of option (A) taking <img decoding=\"async\" style=\"height: 19px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.2\/image166.png\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_102-5\"><\/span>NCERT Solutions class 12 Maths Exercise 10.2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 13 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_App_for_Students\"><\/span>CBSE App for Students<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download\u00a0NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions class 12 Maths Exercise 10.2 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 &#8230; <a title=\"NCERT Solutions class 12 Maths Exercise 10.2\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-2\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 10.2\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1432,281],"tags":[283,1342,321,216],"class_list":["post-4526","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-12","category-ncert-solutions","tag-cbse-study-material","tag-class-12","tag-mathematics","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class 12 Maths Exercise 10.2 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 10.2 in PDF format for free download. 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