{"id":4624,"date":"2016-05-17T11:49:00","date_gmt":"2016-05-17T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-12-3\/"},"modified":"2016-05-17T12:10:20","modified_gmt":"2016-05-17T06:40:20","slug":"ncert-solutions-class-11-maths-exercise-12-3","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-12-3\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 12.3"},"content":{"rendered":"<p style=\"text-align: justify;\"><strong>Exercise 12.3<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>1. Find the coordinates of the point which divides the line segment joining the points <\/strong><img decoding=\"async\" style=\"height: 27px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image001.png\" \/><strong> and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image002.png\" \/><strong> in the ratio: <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) 2: 3 internally, <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) 2: 3 externally.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Let P<img decoding=\"async\" style=\"height: 27px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image003.png\" \/> be any point which divides the line segment joining points A<img decoding=\"async\" style=\"height: 27px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image001.png\" \/><\/p>\n<p style=\"text-align: justify;\">and B<img decoding=\"async\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image002.png\" \/> in the ratio 2: 3 internally. Then<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 204px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 205px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image005.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 41px; width: 197px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, Coordinates of P are <img decoding=\"async\" style=\"height: 45px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Let P<img decoding=\"async\" style=\"height: 27px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image003.png\" \/> be any point which divides the line segment joining points A<img decoding=\"async\" style=\"height: 27px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image001.png\" \/> and B<img decoding=\"async\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image002.png\" \/> in the ratio 2: 3 externally. Then<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 223px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image008.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 232px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 205px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image010.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, Coordinates of P are <img decoding=\"async\" style=\"height: 27px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image011.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>2. Given that P<\/strong><img decoding=\"async\" style=\"height: 27px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image012.png\" \/><strong> Q<\/strong><img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image013.png\" \/><strong> and R<\/strong><img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image014.png\" \/><strong>are collinear. Find the ratio in which Q divides PR.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let Q<img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image013.png\" \/> divides the line segment joining points P<img decoding=\"async\" style=\"height: 27px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image015.png\" \/> and R<img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image014.png\" \/> in the ratio <img decoding=\"async\" style=\"height: 19px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image016.png\" \/> internally. Then<\/p>\n<p style=\"text-align: justify;\">Coordinates of Q are <img decoding=\"async\" style=\"height: 45px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\">According to question, <img decoding=\"async\" style=\"height: 41px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image018.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\/11\/maths\/ch12\/Ex12.3\/image019.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image020.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\/11\/maths\/ch12\/Ex12.3\/image019.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image021.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\/11\/maths\/ch12\/Ex12.3\/image019.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, Q divides the line segment joining the points P and R in the ratio 1: 2.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>3. Find the ratio in which the YZ-plane divides the line segment formed by joining the points <\/strong><img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image023.png\" \/><strong> and <\/strong><img decoding=\"async\" style=\"height: 27px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image024.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let the line segment joining points A<img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image023.png\" \/> and B<img decoding=\"async\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image025.png\" \/> be divided by YZ-plane at a point C in the ratio <img decoding=\"async\" style=\"height: 19px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image016.png\" \/> internally. Then<\/p>\n<p style=\"text-align: justify;\">Coordinates of C are <img decoding=\"async\" style=\"height: 45px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\">According to question, C lies on YZ-plane, i.e., <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image028.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image029.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\/11\/maths\/ch12\/Ex12.3\/image019.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image030.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\/11\/maths\/ch12\/Ex12.3\/image019.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image031.png\" \/><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image019.png\" \/> <img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image032.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, the required ratio is 2: 3.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>4. Using section formula, show that the points A<\/strong><img decoding=\"async\" style=\"height: 27px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image033.png\" \/><strong> B<\/strong><img decoding=\"async\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image034.png\" \/><strong> and C<\/strong><img decoding=\"async\" style=\"height: 45px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image035.png\" \/><strong> are collinear.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let the points B<img decoding=\"async\" style=\"height: 27px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image034.png\" \/> divides the line segment joining A<img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image036.png\" \/> and C<img decoding=\"async\" style=\"height: 45px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image035.png\" \/> in the ratio <img decoding=\"async\" style=\"height: 19px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image016.png\" \/> internally.<\/p>\n<p style=\"text-align: justify;\">Then coordinates of B = <img decoding=\"async\" style=\"height: 82px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 41px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image038.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\/11\/maths\/ch12\/Ex12.3\/image019.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/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\/11\/maths\/ch12\/Ex12.3\/image019.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image040.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>5. Find the coordinates of the points which trisect the line segment joining the points P<\/strong><img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image041.png\" \/><strong> and Q<\/strong><img decoding=\"async\" style=\"height: 27px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image042.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let R and S be two points which trisect the line segment PQ.<\/p>\n<p style=\"text-align: justify;\">Then PR = RS = SQ<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image028.png\" \/>Point R divides the lines segment PQ in the ratio 1: 2.<\/p>\n<p style=\"text-align: justify;\">Then Coordinates of R = <img decoding=\"async\" style=\"height: 51px; width: 307px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image043.png\" \/> = <img decoding=\"async\" style=\"height: 27px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image044.png\" \/><\/p>\n<p style=\"text-align: justify;\">Again, Point S divides the line segment PQ in the ratio 2: 1.<\/p>\n<p style=\"text-align: justify;\">Then Coordinates of S = <img decoding=\"async\" style=\"height: 51px; width: 304px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image045.png\" \/> = <img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch12\/Ex12.3\/image046.png\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Exercise 12.3 1. Find the coordinates of the point which divides the line segment joining the points and in the ratio: (i) 2: 3 internally, (ii) 2: 3 externally. Ans. (i) Let P be any point which divides the line segment joining points A and B in the ratio 2: 3 internally. Then Therefore, Coordinates &#8230; <a title=\"NCERT Solutions class-11 Maths Exercise 12.3\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-12-3\/\" aria-label=\"More on NCERT Solutions class-11 Maths Exercise 12.3\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4624","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-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-11 Maths Exercise 12.3 | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-12-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Exercise 12.3 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 12.3 1. Find the coordinates of the point which divides the line segment joining the points and in the ratio: (i) 2: 3 internally, (ii) 2: 3 externally. Ans. (i) Let P be any point which divides the line segment joining points A and B in the ratio 2: 3 internally. Then Therefore, Coordinates ... 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