{"id":4527,"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-10-4\/"},"modified":"2018-05-08T17:23:30","modified_gmt":"2018-05-08T11:53:30","slug":"ncert-solutions-class-12-maths-exercise-10-4","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-4\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 10.4"},"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-10-4\/#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-10-4\/#2_Find_a_unit_vector_perpendicular_to_each_of_the_vectors_and_where_and\" >2. Find a unit vector perpendicular to each of the vectors \u00a0and \u00a0where \u00a0and \u00a0<\/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-10-4\/#3_If_a_unit_vector_makes_an_angle_with_with_and_an_acute_angle_with_then_find_and_hence_the_components_of\" >3. If a unit vector \u00a0makes an angle \u00a0with \u00a0\u00a0with \u00a0and an acute angle \u00a0with \u00a0then find \u00a0and hence, the components of .<\/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-10-4\/#4_Show_that\" >4. Show that \u00a0<\/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-10-4\/#5_Find_and_if\" >5. Find \u00a0and \u00a0if \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-10-4\/#6_Given_that_and_What_can_you_conclude_about_the_vectors_and\" >6. Given that \u00a0and \u00a0What can you conclude about the vectors \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-10-4\/#7_Let_the_vectors_be_given_as_then_show_that\" >7. Let the vectors \u00a0be given as \u00a0then show that \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-10-4\/#8_It_either_and_then_Is_the_converse_true_Justify_your_answer_with_an_example\" >8. It either \u00a0and \u00a0then \u00a0Is the converse true? Justify your answer with an example.<\/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-10-4\/#NCERT_Solutions_class_12_Maths_Exercise_104\" >NCERT Solutions class 12 Maths Exercise 10.4<\/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-10-4\/#9_Find_the_area_of_the_triangle_with_vertices_A_1_1_2_B_2_3_5_and_C_1_5_5\" >9. Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).<\/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-10-4\/#NCERT_Solutions_class_12_Maths_Exercise_104-2\" >NCERT Solutions class 12 Maths Exercise 10.4<\/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-10-4\/#10_Find_the_area_of_the_parallelogram_whose_adjacent_sides_are_determined_by_the_vectors_and\" >10. Find the area of the parallelogram whose adjacent sides are determined by 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-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-4\/#NCERT_Solutions_class_12_Maths_Exercise_104-3\" >NCERT Solutions class 12 Maths Exercise 10.4<\/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-10-4\/#11_Let_the_vectors_and_such_that_then_is_a_unit_vector_if_the_angle_between_and_is\" >11. Let the vectors \u00a0and \u00a0such that \u00a0then \u00a0is a unit vector, if the angle between \u00a0and \u00a0is:<\/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-10-4\/#NCERT_Solutions_class_12_Maths_Exercise_104-4\" >NCERT Solutions class 12 Maths Exercise 10.4<\/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-10-4\/#12_Area_of_a_rectangle_having_vertices_A_B_C_and_D_with_position_vectors_and_respectively_is\" >12. Area of a rectangle having vertices A, B, C and D with position vectors \u00a0and \u00a0respectively is:<\/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-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-4\/#NCERT_Solutions_class_12_Maths_Exercise_104-5\" >NCERT Solutions class 12 Maths Exercise 10.4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-10-4\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 10.4 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 10.4\" width=\"214\" height=\"274\" \/><\/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: center;\"><strong>Vector Algebra<\/strong><\/p>\n<p style=\"text-align: center;\">Exercise 10.4<\/p>\n<p><strong>1. Find <\/strong><img decoding=\"async\" style=\"height: 32px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image001.png\" \/><strong>\u00a0if <\/strong><img decoding=\"async\" style=\"height: 27px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image002.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image003.png\" \/><strong>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 27px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image004.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image005.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 83px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image006.png\" \/><\/p>\n<p>Expanding along first row,<\/p>\n<p><img decoding=\"async\" style=\"height: 48px; width: 241px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image007.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 29px; width: 233px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image008.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image009.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 36px; width: 311px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image011.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"2_Find_a_unit_vector_perpendicular_to_each_of_the_vectors_and_where_and\"><\/span><strong>2. Find a unit vector perpendicular to each of the vectors <\/strong><img decoding=\"async\" style=\"height: 23px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image012.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 23px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image013.png\" \/><strong>\u00a0where <\/strong><img decoding=\"async\" style=\"height: 27px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image014.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image015.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 27px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image014.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image016.png\" \/><\/p>\n<p>On Adding\u00a0 <img decoding=\"async\" style=\"height: 23px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image017.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image018.png\" \/>\u00a0+ <img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image019.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image020.png\" \/><\/p>\n<p>On Subtracting\u00a0 <img decoding=\"async\" style=\"height: 23px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image021.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image018.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 11px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image022.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image023.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image024.png\" \/><\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 83px; width: 184px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image025.png\" \/><\/p>\n<p>Expanding along first row = <img decoding=\"async\" style=\"height: 29px; width: 195px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image026.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image028.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 36px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image029.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 24px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image030.png\" \/><\/p>\n<p>Therefore, a unit vector perpendicular to both <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image031.png\" \/>\u00a0\u00a0and <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image032.png\" \/>\u00a0is<\/p>\n<p><img decoding=\"async\" style=\"height: 63px; width: 184px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image033.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image034.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image035.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"3_If_a_unit_vector_makes_an_angle_with_with_and_an_acute_angle_with_then_find_and_hence_the_components_of\"><\/span><strong>3. If a unit vector <\/strong><img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image036.png\" \/><strong>\u00a0makes an angle <\/strong><img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image037.png\" \/><strong>\u00a0with <\/strong><img decoding=\"async\" style=\"height: 27px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image038.png\" \/><strong>\u00a0<\/strong><img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image039.png\" \/><strong>\u00a0with <\/strong><img decoding=\"async\" style=\"height: 27px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image040.png\" \/><strong>\u00a0and an acute angle <\/strong><img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image041.png\" \/><strong>\u00a0with <\/strong><img decoding=\"async\" style=\"height: 27px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image042.png\" \/><strong>\u00a0then find <\/strong><img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image041.png\" \/><strong>\u00a0and hence, the components of <\/strong><img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image036.png\" \/><strong>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Let <img decoding=\"async\" style=\"height: 27px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image043.png\" \/>\u00a0be a unit vector.\u00a0 \u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 35px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image044.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 29px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image045.png\" \/><\/p>\n<p>Squaring both sides,\u00a0 <img decoding=\"async\" style=\"height: 24px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image046.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p>Given: Angle between vectors <img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image036.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image047.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image048.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 57px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image049.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image050.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image051.png\" \/>\u00a0\u2026\u2026\u2026.(iii)<\/p>\n<p>Again, given Angel between vectors <img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image036.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image052.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image053.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 57px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image054.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 163px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image055.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 44px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image056.png\" \/>\u00a0\u2026\u2026\u2026.(iv)<\/p>\n<p>Again, given Angel between vectors <img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image036.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 27px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image057.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 21px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image058.png\" \/>\u00a0where <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image041.png\" \/>\u00a0is acute angle.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 57px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image059.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 173px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image060.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image061.png\" \/>\u00a0\u2026\u2026\u2026.(v)<\/p>\n<p>Putting the values of <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image062.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image063.png\" \/>\u00a0in eq. (ii),<\/p>\n<p><img decoding=\"async\" style=\"height: 41px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image064.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image065.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image066.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image067.png\" \/><\/p>\n<p>Since <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image041.png\" \/>\u00a0is acute angle, therefore <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image068.png\" \/>\u00a0is positive and hence <img decoding=\"async\" style=\"height: 41px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image069.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image070.png\" \/><\/p>\n<p>From eq. (v), <img decoding=\"async\" style=\"height: 41px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image071.png\" \/><\/p>\n<p>Putting values of <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image062.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image063.png\" \/>\u00a0in eq. (i), <img decoding=\"async\" style=\"height: 44px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image072.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0Components of <img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image036.png\" \/>\u00a0are coefficients of <img decoding=\"async\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image073.png\" \/>\u00a0in <img decoding=\"async\" style=\"height: 24px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image036.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 44px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image074.png\" \/>\u00a0and angle <img decoding=\"async\" style=\"height: 41px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image070.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"4_Show_that\"><\/span><strong>4. Show that <\/strong><img decoding=\"async\" style=\"height: 32px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image075.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>L.H.S. = <img decoding=\"async\" style=\"height: 32px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image076.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 23px; width: 163px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image077.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 32px; width: 232px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image078.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 23px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image079.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 23px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image080.png\" \/>\u00a0= R.H.S.<\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"5_Find_and_if\"><\/span><strong>5. Find <\/strong><img decoding=\"async\" style=\"height: 19px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image081.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image082.png\" \/><strong>\u00a0if <\/strong><img decoding=\"async\" style=\"height: 35px; width: 221px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image083.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 35px; width: 219px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image084.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 83px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image085.png\" \/><\/p>\n<p>Expanding along first row,<\/p>\n<p><img decoding=\"async\" style=\"height: 29px; width: 269px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image086.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image087.png\" \/><\/p>\n<p>Comparing the coefficients of <img decoding=\"async\" style=\"height: 27px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image073.png\" \/>\u00a0on both sides, we have<\/p>\n<p><img decoding=\"async\" style=\"height: 21px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image088.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 21px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image089.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p>And <img decoding=\"async\" style=\"height: 19px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image090.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(iii)<\/p>\n<p>From eq. (ii),\u00a0 <img decoding=\"async\" style=\"height: 21px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image089.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image091.png\" \/><\/p>\n<p>From eq. (iii),\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image090.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image092.png\" \/><\/p>\n<p>Putting the values of <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image082.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image081.png\" \/>\u00a0in eq. (i),<\/p>\n<p><img decoding=\"async\" style=\"height: 45px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image093.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image094.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a00 = 0<\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 41px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image091.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image092.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"6_Given_that_and_What_can_you_conclude_about_the_vectors_and\"><\/span><strong>6. Given that <\/strong><img decoding=\"async\" style=\"height: 23px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image095.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 23px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image096.png\" \/><strong>\u00a0What can you conclude about the vectors <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image031.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 23px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image097.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 23px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image095.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image098.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image099.png\" \/>\u00a0 or <img decoding=\"async\" style=\"height: 32px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image100.png\" \/>\u00a0\u00a0or <img decoding=\"async\" style=\"height: 19px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image101.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image102.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image103.png\" \/>\u00a0 or <img decoding=\"async\" style=\"height: 23px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image104.png\" \/>\u00a0\u00a0or vector <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image031.png\" \/>\u00a0is perpendicular to <img decoding=\"async\" style=\"height: 23px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image105.png\" \/>\u00a0\u2026..(i)<\/p>\n<p>Again, given <img decoding=\"async\" style=\"height: 23px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image106.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image107.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image108.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image099.png\" \/>\u00a0 or <img decoding=\"async\" style=\"height: 32px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image100.png\" \/>\u00a0\u00a0or <img decoding=\"async\" style=\"height: 19px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image109.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image110.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image103.png\" \/>\u00a0\u00a0\u00a0 or <img decoding=\"async\" style=\"height: 23px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image104.png\" \/>\u00a0\u00a0or vector <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image031.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image032.png\" \/>\u00a0are collinear or parallel. \u2026..(ii)<\/p>\n<p>Since, vectors <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image031.png\" \/>\u00a0&amp; <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image032.png\" \/>\u00a0are perpendicular to each other as well as parallel are not possible. ..(iii)<\/p>\n<p>Therefore, from eq. (i), (ii) and (iii),\u00a0 either <img decoding=\"async\" style=\"height: 23px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image111.png\" \/>\u00a0\u00a0or <img decoding=\"async\" style=\"height: 23px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image112.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image095.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 23px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image106.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"7_Let_the_vectors_be_given_as_then_show_that\"><\/span><strong>7. Let the vectors <\/strong><img decoding=\"async\" style=\"height: 25px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image113.png\" \/><strong>\u00a0be given as <\/strong><img decoding=\"async\" style=\"height: 28px; width: 287px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image114.png\" \/><strong>\u00a0then show that <\/strong><img decoding=\"async\" style=\"height: 32px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image115.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Given: Vector <img decoding=\"async\" style=\"height: 28px; width: 237px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image116.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 28px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image117.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 29px; width: 259px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image118.png\" \/><\/p>\n<p>Now L.H.S. = <img decoding=\"async\" style=\"height: 83px; width: 268px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image119.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 83px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image120.png\" \/>\u00a0+ <img decoding=\"async\" style=\"height: 83px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image121.png\" \/><\/p>\n[By Property of Determinants]\n<p>= <img decoding=\"async\" style=\"height: 23px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image122.png\" \/>\u00a0= R.H.S.<\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"8_It_either_and_then_Is_the_converse_true_Justify_your_answer_with_an_example\"><\/span><strong>8. It either <\/strong><img decoding=\"async\" style=\"height: 23px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image111.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 25px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image123.png\" \/><strong>\u00a0then <\/strong><img decoding=\"async\" style=\"height: 23px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image124.png\" \/><strong>\u00a0Is the converse true? Justify your answer with an example.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Given: Either <img decoding=\"async\" style=\"height: 23px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image111.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 23px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image112.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image125.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 32px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image126.png\" \/>\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image127.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image128.png\" \/>\u00a0 [Using eq. (i)]\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image129.png\" \/>\u00a0[By definition of zero vector]\n<p>But the converse is not true.<\/p>\n<p>Let <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image130.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image131.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image031.png\" \/>\u00a0is a non-zero vector.<\/p>\n<p>Let <img decoding=\"async\" style=\"height: 35px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image132.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 208px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image133.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image032.png\" \/>\u00a0is a non-zero vector.<\/p>\n<p>But <img decoding=\"async\" style=\"height: 83px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image134.png\" \/><\/p>\n<p>Taking 2 common from R<sub>3<\/sub> = <img decoding=\"async\" style=\"height: 83px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image135.png\" \/>\u00a0\u00a0[<img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image136.png\" \/>\u00a0R<sub>2<\/sub> and R<sub>3<\/sub> are identical]\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_104\"><\/span>NCERT Solutions class 12 Maths Exercise 10.4<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"9_Find_the_area_of_the_triangle_with_vertices_A_1_1_2_B_2_3_5_and_C_1_5_5\"><\/span><strong>9. Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Vertices of <img decoding=\"async\" style=\"height: 19px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image137.png\" \/>\u00a0are A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0Position vector of point A = (1, 1, 2) = <img decoding=\"async\" style=\"height: 27px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image138.png\" \/><\/p>\n<p>Position vector of point B = (2, 3, 5) = <img decoding=\"async\" style=\"height: 27px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image139.png\" \/><\/p>\n<p>Position vector of point C = (1, 5, 5) = <img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image140.png\" \/><\/p>\n<p>Now <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image141.png\" \/>\u00a0= Position vector of point B \u2013 Position vector of point A<\/p>\n<p>=\u00a0 <img decoding=\"async\" style=\"height: 27px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image139.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 35px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image142.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image139.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image143.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image144.png\" \/><\/p>\n<p>And <img decoding=\"async\" style=\"height: 23px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image145.png\" \/>\u00a0= Position vector of point C \u2013 Position vector of point A<\/p>\n<p>=\u00a0 <img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image140.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 35px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image142.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image140.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image143.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image146.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image141.png\" \/>\u00a0x <img decoding=\"async\" style=\"height: 23px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image145.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 67px; width: 70px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image147.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 175px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image148.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 24px; width: 70px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image149.png\" \/><\/p>\n<p>Now Area of triangle ABC = <img decoding=\"async\" style=\"height: 41px; width: 185px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image150.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image151.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_104-2\"><\/span>NCERT Solutions class 12 Maths Exercise 10.4<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"10_Find_the_area_of_the_parallelogram_whose_adjacent_sides_are_determined_by_the_vectors_and\"><\/span><strong>10. Find the area of the parallelogram whose adjacent sides are determined by the vectors <\/strong><img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image152.png\" \/><strong>\u00a0<\/strong><img decoding=\"async\" style=\"height: 27px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image153.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image154.png\" \/><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Given: Vectors representing two adjacent sides of a parallelogram are<\/p>\n<p><img decoding=\"async\" style=\"height: 27px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image155.png\" \/>\u00a0and\u00a0 <img decoding=\"async\" style=\"height: 27px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image156.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 74px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image157.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 29px; width: 208px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image158.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 27px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image159.png\" \/><\/p>\n<p>Now Area of parallelogram = <img decoding=\"async\" style=\"height: 32px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image160.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 24px; width: 204px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image161.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_104-3\"><\/span>NCERT Solutions class 12 Maths Exercise 10.4<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"11_Let_the_vectors_and_such_that_then_is_a_unit_vector_if_the_angle_between_and_is\"><\/span><strong>11. Let the vectors <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image031.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image032.png\" \/><strong>\u00a0such that <\/strong><img decoding=\"async\" style=\"height: 45px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image162.png\" \/><strong>\u00a0then <\/strong><img decoding=\"async\" style=\"height: 23px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image163.png\" \/><strong>\u00a0is a unit vector, if the angle between <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image031.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image032.png\" \/><strong>\u00a0is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(A) <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image164.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image039.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image037.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image165.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong>Given: <img decoding=\"async\" style=\"height: 45px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image166.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 23px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image163.png\" \/>\u00a0is a unit vector.<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image167.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 32px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image168.png\" \/>, where <img decoding=\"async\" style=\"height: 19px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image041.png\" \/>\u00a0is the angle between <img decoding=\"async\" style=\"height: 23px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image031.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 23px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image105.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 47px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image169.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 23px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image170.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 44px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image171.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image172.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image027.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image173.png\" \/><\/p>\n<p>Therefore, option (B) is correct.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_104-4\"><\/span>NCERT Solutions class 12 Maths Exercise 10.4<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"12_Area_of_a_rectangle_having_vertices_A_B_C_and_D_with_position_vectors_and_respectively_is\"><\/span><strong>12. Area of a rectangle having vertices A, B, C and D with position vectors <\/strong><img decoding=\"async\" style=\"height: 41px; width: 237px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image174.png\" \/><strong>\u00a0and <\/strong><img decoding=\"async\" style=\"height: 41px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image175.png\" \/><strong>\u00a0respectively is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(A) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image176.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(B) 1<\/strong><\/p>\n<p><strong>(C) 2<\/strong><\/p>\n<p><strong>(D) 4<\/strong><\/p>\n<p><strong>Ans. <\/strong>Given: ABCD is a rectangle.<\/p>\n<p>Now <img decoding=\"async\" style=\"height: 21px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image141.png\" \/>\u00a0= Position vector of point B \u2013 Position vector of point A<\/p>\n<p>=\u00a0 <img decoding=\"async\" style=\"height: 40px; width: 164px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image177.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 34px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image178.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image179.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0AB = <img decoding=\"async\" style=\"height: 32px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image180.png\" \/><\/p>\n<p>And\u00a0 <img decoding=\"async\" style=\"height: 21px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image181.png\" \/>\u00a0= Position vector of point D \u2013 Position vector of point A<\/p>\n<p>=\u00a0 <img decoding=\"async\" style=\"height: 39px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image182.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 37px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image183.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 24px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image184.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0AD = <img decoding=\"async\" style=\"height: 30px; width: 154px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image185.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex10.4\/image010.png\" \/>\u00a0Area of rectangle ABCD = Length x Breadth = AB x AD = 2 x 1 = 2 sq. units<\/p>\n<p>Therefore, option (C) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_104-5\"><\/span>NCERT Solutions class 12 Maths Exercise 10.4<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 10.4 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. 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