{"id":60231,"date":"2022-01-29T17:49:35","date_gmt":"2022-01-29T12:19:35","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=60231"},"modified":"2022-06-16T15:17:11","modified_gmt":"2022-06-16T09:47:11","slug":"study-materials-ncert-exemplar-solutions-class-11-maths-chapter-12-introduction-to-three-dimensional-geometry","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/","title":{"rendered":"NCERT Exemplar Solutions for Class 11 Maths Chapter 12 &#8211; Introduction to Three Dimensional Geometry"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\">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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#121_Introduction\" title=\"12.1 Introduction\">12.1 Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#122_Coordinate_Axes_and_Coordinate_Planes_in_Three_Dimensional_Space\" title=\"12.2 Coordinate Axes and Coordinate Planes in Three Dimensional Space\">12.2 Coordinate Axes and Coordinate Planes in Three Dimensional Space<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#123_Coordinates_of_a_Point_in_Space\" title=\"12.3 Coordinates of a Point in Space\">12.3 Coordinates of a Point in Space<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#124_Distance_between_Two_Points\" title=\"12.4 Distance between Two Points\">12.4 Distance between Two Points<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#125_Section_Formula\" title=\"12.5 Section Formula\">12.5 Section Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#A_few_points_on_Chapter_12_Introduction_To_Three_Dimensional_Geometry\" title=\"A few points on Chapter 12 Introduction To Three Dimensional Geometry\">A few points on Chapter 12 Introduction To Three Dimensional Geometry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#Frequently_Asked_Questions\" title=\"Frequently Asked Questions\">Frequently Asked Questions<\/a><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#Explain_the_concept_of_3D_Geometry_covered_in_the_Chapter_12_of_NCERT_Exemplar_Solutions_for_Class_11_Maths\" title=\"Explain the concept of 3D Geometry covered in the Chapter 12 of NCERT Exemplar Solutions for Class 11 Maths.\">Explain the concept of 3D Geometry covered in the Chapter 12 of NCERT Exemplar Solutions for Class 11 Maths.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#Where_can_I_get_the_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_12\" title=\"Where can I get the NCERT Exemplar Solutions for Class 11 Maths Chapter 12?\">Where can I get the NCERT Exemplar Solutions for Class 11 Maths Chapter 12?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/#Why_Opt_for_Infinity_Learn\" title=\"Why Opt for Infinity Learn?\">Why Opt for Infinity Learn?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 12: Introduction to Three Dimensional Geometry, <\/span><span style=\"font-weight: 400;\">which includes thorough solutions for reference. All of the unsolved questions from the textbook&#8217;s exercises are answered here. The NCERT Exemplar Solutions for Class 11 provide useful solutions for improving conceptual knowledge and help in entrance examinations like <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/jee\" target=\"_blank\" rel=\"noopener\">JEE mains and advanced<\/a><\/span><\/strong>.<\/span><\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-174022 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/01\/class-7-math-ncert-solutions.webp\" alt=\"NCERT Exemplar Solutions for Class 11 Maths Chapter 12\" width=\"626\" height=\"417\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/01\/class-7-math-ncert-solutions.webp 626w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/01\/class-7-math-ncert-solutions-300x200.webp 300w\" sizes=\"(max-width: 626px) 100vw, 626px\" \/><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/\" target=\"_blank\" rel=\"noopener\">NCERT Exemplar Solutions<\/a><\/span><\/strong> for Class 11. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.<\/span><\/p>\n<p><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.<\/span><span style=\"font-weight: 400;\"> <\/span><\/span><\/p>\n<p><span style=\"font-size: 12pt;\">\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? 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wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/60231\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/securepdfs\/2022\/01\/Class11_Math_Chapter12DE-12.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"\/surge\/?pdfemb-serveurl=https%3A%2F%2Finfinitylearn.com%2Fsurge%2Fwp-content%2Fuploads%2Fsecurepdfs%2F2022%2F01%2FClass11_Math_Chapter12DE-12.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-download-nonce=\"7e6fc0129c\" data-disablerightclick=\"on\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Class11_Math_Chapter12(DE-12)<br\/><\/a><\/span><\/p>\n<p><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">The topics and sub-topics that are covered in the NCERT Maths textbook for Class 11 Chapter 12 Introduction to Three Dimensional Geometry that is included in the syllabus of second term CBSE Class 11 Maths Syllabus 2021-22 are<\/span> <span style=\"font-weight: 400;\">listed below: <\/span><\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"121_Introduction\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\"><b>12.1 Introduction<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Through this section students comes to know about the topic of Coordinate axes, Coordinate planes in real life, Coordinates of the point in the three-dimensional space, Geometry in three-dimensional space.<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"122_Coordinate_Axes_and_Coordinate_Planes_in_Three_Dimensional_Space\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\"><b>12.2 Coordinate Axes and Coordinate Planes in Three Dimensional Space<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">In this section, the rectangular coordinate system, the naming of a coordinate plane, and different notations in coordinate planes are explained.<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Rahul was cycling home from a basketball game at a nearby stadium when he bumped into the bulkhead to avoid a dog that had run down the road. Sadly, his bicycle was glued to the separator. When he was unable to remove the bicycle on his own, he asked for the services of a friend who lived in the neighborhood. Rahul later used a topographical map to locate his friend&#8217;s residence. He cycled his bicycle 200 meters south and 550 meters west from where he left it. He had also hiked uphill from 600 meters to 650 meters above sea level, according to the map. What is the position vector of the Kapur farm if we use the location of Rahul&#8217;s bicycle as the origin of coordinates?<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"123_Coordinates_of_a_Point_in_Space\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\"><b>12.3 Coordinates of a Point in Space<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">The coordinates [x, y, and z] in the space with the help of a few examples are explained in this section.<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">A two-dimensional grid representing the room can be sketched and an appropriate unit of measurement should be selected if a student is planning to framework pieces of furniture in a drawing-room. Let&#8217;s consider the horizontal distance x, the vertical distance to x position is y, and the initial point origin. If the room&#8217;s width is 10 meters, any point within it can be represented as <\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"124_Distance_between_Two_Points\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\"><b>12.4 Distance between Two Points<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">In this section, students learn about the distance formulae to find the distance between three points in a three-dimensional coordinate system with the help of solved problems.<\/span><\/p>\n<p><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">By using the distance formulae, the distance between the point P from the axes <\/span><span style=\"font-weight: 400;\"> is calculated, where P is any object placed in a coordinate plane.<\/span><\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"125_Section_Formula\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\"><b>12.5 Section Formula<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">In this section, students learn the section formula along with its different cases which are used in three-dimensional geometry. Many examples are given for a better understanding of these formulae.<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">The total number of questions in the exercises of chapter 12 are listed below:<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Exercise 12.1 Solutions: 4 Questions<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Exercise 12.2 Solutions: 5 Questions<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Exercise 12.3 Solutions: 5 Questions<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Miscellaneous Exercise On Chapter 12 Solutions: 6 Questions<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"A_few_points_on_Chapter_12_Introduction_To_Three_Dimensional_Geometry\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\"><b>A few points on Chapter 12 Introduction To Three Dimensional Geometry<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">A cartesian coordinate system in three-dimensional geometry is comprised of three mutually perpendicular lines called the x, y, and z-axes. The measuring unit of length of all is the same.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">The pair of axes in the three planes that are XY-plane, YZ-plane, and ZX-plane is known as the axes of the coordinate planes.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">If the three coordinate planes XY-plane, YZ-plane, and ZX-plane, divide the coordinate space into eight parts then it is known as octants.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">In three-dimensional geometry, the coordinates of a point P <\/span><span style=\"font-weight: 400;\"> are expressed as an ordered triplet. The distances between the YZ, ZX, and XY planes are represented by x, y, and z.<\/span><\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Internally and externally, the coordinates of point R divide the line segment connecting two points.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">The subject specialists who created the NCERT Exemplar Solutions for Class 11 Maths have deep knowledge of the question paper format and types of questions that will appear in the second term exam. These solutions offer alternative techniques and explanations for solving issues, giving students confidence as they approach the term &#8211; II exam. Solving a large number of difficult problems also improves pupils&#8217; mathematical abilities. The answers cover all of the questions that a student needs and should know in order to take the second-term exam.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions\"><\/span><span style=\"font-size: 12pt;\"><b>Frequently Asked Questions<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Explain_the_concept_of_3D_Geometry_covered_in_the_Chapter_12_of_NCERT_Exemplar_Solutions_for_Class_11_Maths\"><\/span>Explain the concept of 3D Geometry covered in the Chapter 12 of NCERT Exemplar Solutions for Class 11 Maths.<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\t3D Geometry is a discipline of mathematics that deals with the study of three-dimensional coordinate systems and the study of points, lines, and solid objects. It will teach students how to use the z-coordinate in conjunction with the x and y coordinates to calculate the exact location of a point in the 3D coordinate plane. It is a fundamental theory with applications in different fields of science and higher mathematics. The concept of trigonometric ratios is useful in 3D geometry.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Where_can_I_get_the_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_12\"><\/span>Where can I get the NCERT Exemplar Solutions for Class 11 Maths Chapter 12?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tOur experts' NCERT Exemplar Solutions are the greatest reference resource for students who want to do well in their term-wise exams. These solutions include in-depth explanations for each idea discussed in the chapter. Students who are having problems understanding exercise-specific questions can use the online solutions to get their questions answered right away. Our experts produced chapter-by-chapter and exercise-by-exercise solutions with the goal of assisting students of all intellect levels.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Why_Opt_for_Infinity_Learn\"><\/span>Why Opt for Infinity Learn?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Explain the concept of 3D Geometry covered in the Chapter 12 of NCERT Exemplar Solutions for Class 11 Maths.\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"3D Geometry is a discipline of mathematics that deals with the study of three-dimensional coordinate systems and the study of points, lines, and solid objects. It will teach students how to use the z-coordinate in conjunction with the x and y coordinates to calculate the exact location of a point in the 3D coordinate plane. It is a fundamental theory with applications in different fields of science and higher mathematics. The concept of trigonometric ratios is useful in 3D geometry.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Where can I get the NCERT Exemplar Solutions for Class 11 Maths Chapter 12?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Our experts' NCERT Exemplar Solutions are the greatest reference resource for students who want to do well in their term-wise exams. These solutions include in-depth explanations for each idea discussed in the chapter. Students who are having problems understanding exercise-specific questions can use the online solutions to get their questions answered right away. Our experts produced chapter-by-chapter and exercise-by-exercise solutions with the goal of assisting students of all intellect levels.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Why Opt for Infinity Learn?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n<p><strong><span style=\"color: #0000ff;\">Question:<\/span> <\/strong>Discuss the topics covered in the Chapter 12 of NCERT Exemplar Solutions for Class 11 Maths.<\/p>\n<p><strong><span style=\"color: #ff0000;\">Answer:<\/span> <\/strong>Following are the topics that are discussed in Chapter 12 of NCERT Maths Solutions for Class 11:<\/p>\n<ol>\n<li>Introduction<\/li>\n<li>Coordinate axes and coordinate planes in Three Dimensional Space<\/li>\n<li>Coordinates of a Point in Space<\/li>\n<li>Distance between Two Points<\/li>\n<li>Section Formula<\/li>\n<\/ol>\n<p><strong><span style=\"color: #0000ff;\">Infinity Learn App<\/span><\/strong><\/p>\n<p>Now you can find answers to all your subject queries &amp; prepare for your Exams on our <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.infinitylearn.learn\" target=\"_blank\" rel=\"noopener\">Learning App<\/a><\/span> &#8211; Infinity Learn.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 12: Introduction to Three Dimensional Geometry, which includes [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Exemplar Solutions for Class 11 Maths Chapter 12","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 12: Introduction to Three Dimensional Geometry, which includes thorough solutions for reference.","custom_permalink":"study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-12-introduction-to-three-dimensional-geometry\/"},"categories":[107,113,105],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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