{"id":60453,"date":"2022-01-29T23:23:56","date_gmt":"2022-01-29T17:53:56","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=60453"},"modified":"2025-05-19T11:12:41","modified_gmt":"2025-05-19T05:42:41","slug":"ncert-exemplar-solutions-for-class-12-maths-chapter-11-three-dimensional-geometry","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/","title":{"rendered":"NCERT Exemplar Solutions for Class 12 Maths Chapter 11 &#8211; 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-12\/maths\/chapter-11-three-dimensional-geometry\/#The_topics_and_subtopics_covered_in_Chapter_11-_Three_Dimensional_Geometry_of_NCERT_Exemplar_Solutions_for_Class_12_are_as_follows\" title=\"The topics and subtopics covered in Chapter 11- Three Dimensional Geometry of NCERT Exemplar Solutions for Class 12 are as follows:\">The topics and subtopics covered in Chapter 11- Three Dimensional Geometry of NCERT Exemplar Solutions for Class 12 are as follows:<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/#NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_11-_Three_Dimensional_Geometry\" title=\"NCERT Exemplar Solutions for Class 12 Maths Chapter 11- Three Dimensional Geometry\">NCERT Exemplar Solutions for Class 12 Maths Chapter 11- Three Dimensional Geometry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/#Key_Features_of_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_11-_Three_Dimensional_Geometry\" title=\"Key Features of NCERT Exemplar Solutions for Class 12 Maths Chapter 11- Three Dimensional Geometry\">Key Features of NCERT Exemplar Solutions for Class 12 Maths Chapter 11- Three Dimensional Geometry<\/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-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/#What_is_three_dimensional_geometry_in_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_11\" title=\"What is three dimensional geometry in NCERT Exemplar Solutions for Class 12 Maths Chapter 11?\">What is three dimensional geometry in NCERT Exemplar Solutions for Class 12 Maths Chapter 11?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/#Is_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_11_the_best_study_material_for_the_students_during_revision\" title=\"Is NCERT Exemplar Solutions for Class 12 Maths Chapter 11 the best study material for the students during revision?\">Is NCERT Exemplar Solutions for Class 12 Maths Chapter 11 the best study material for the students during revision?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/#Why_Opt_for_Infinity_Learn\" title=\"Why Opt for Infinity Learn?\">Why Opt for Infinity Learn?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/#What_are_the_important_topics_covered_in_Chapter_11_of_NCERT_Exemplar_Solutions_for_Class_12_Maths\" title=\"What are the important topics covered in Chapter 11 of NCERT Exemplar Solutions for Class 12 Maths\">What are the important topics covered in Chapter 11 of NCERT Exemplar Solutions for Class 12 Maths<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/#Infinity_Learn_App\" title=\"Infinity Learn App\">Infinity Learn App<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry, which includes thorough solutions for reference. All of the questions from the textbook&#8217;s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Exemplar Solutions for Class 12 provide useful solutions for improving conceptual knowledge and preparing for exams like <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/jee\" target=\"_blank\" rel=\"noopener\"><strong>JEE<\/strong><\/a><\/span>.<\/span><\/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 NCERT Exemplar Solutions for Class 12. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 12 pupils perform well in upcoming competitive exams.<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">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><\/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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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\/Class12_Maths_Chapter11DE-27.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%2FClass12_Maths_Chapter11DE-27.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=\"1d2fe5b322\" data-disablerightclick=\"on\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Class12_Maths_Chapter11(DE-27)<br\/><\/a><\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_topics_and_subtopics_covered_in_Chapter_11-_Three_Dimensional_Geometry_of_NCERT_Exemplar_Solutions_for_Class_12_are_as_follows\"><\/span><span style=\"font-size: 14pt; color: #0000ff;\"><b>The topics and subtopics covered in Chapter 11- Three Dimensional Geometry of NCERT Exemplar Solutions for Class 12 are as follows:<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.1 Introduction<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.2 Direction Cosines and Direction Ratios of a Line<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.2.1 Relation between the direction cosines of a line<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.2.2 Direction cosines of a line passing through two points<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.3 Equation of a Line in Space<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.3.1 Equation of a line through a given point and parallel to a given vector b.<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.3.2 Equation of a line passing through two given points<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.4 Angle between Two Lines<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.5 Shortest Distance between Two Lines<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.5.1 Distance between two skew lines<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.5.2 Distance between parallel lines<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.6 Plane<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.6.1 Equation of a plane in normal form<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.6.2 Equation of a plane perpendicular to a given vector, passing through a given point<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.6.3 Equation of a plane passing through three non-collinear points<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.6.4 Intercept form of the equation of a plane<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.6.5 Plane passing through the intersection of two given planes<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.7 Coplanarity of Two Lines<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.8 Angle between Two Planes<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.9 Distance of a Point from a Plane<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">11.10 Angle between a Line and a Plane<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_11-_Three_Dimensional_Geometry\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\"><b>NCERT Exemplar Solutions for Class 12 Maths Chapter 11- Three Dimensional Geometry<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">According to the new CBSE Syllabus 2021-22, the chapter Three Dimensional Geometry is part of the unit Vectors and Three\u2013Dimensional Geometry in term II. It accounts for 14 of the total marks. This chapter includes three activities, as well as a random, practice to assist students to grasp the fundamentals of Three Dimensional Geometry. The following are some of the topics covered in Chapter 11 of NCERT Exemplar Solutions for Class 12 Maths:<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">The cosines of the angles formed by a line with the positive directions of the coordinate axes are called the direction cosines of a line.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">If l, m, n are the direction cosines of a line, then l^2+m^2+n^2 = 1<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">A line&#8217;s direction ratios are the numbers that are proportional to the line&#8217;s direction cosines.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Skewed lines are lines that are neither parallel nor intersecting in space. They are positioned on distinct planes.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; font-size: 12pt;\">Angle between skew lines is the angle formed by two intersecting lines drawn parallel to one other from any point (ideally through the origin).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">If l1 , m1, n1 and l2, m2, n2 are the direction cosines of two lines; and \u03b8 is the acute angle between the two lines; then cos\u03b8 = |l<\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">l<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + m1m2 + n1n2|<\/span><\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">These are some of the topics covered in the three-dimensional geometry chapter. NCERT Exemplar Solutions can be used as a quick reference to help students understand complicated concepts. Refer to the NCERT Textbook and NCERT Exemplar Solutions of Class 12 Maths for further information on the chapter.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Key_Features_of_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_11-_Three_Dimensional_Geometry\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\"><b>Key Features of NCERT Exemplar Solutions for Class 12 Maths Chapter 11- Three Dimensional Geometry<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Students who study Class 12 Three Dimensional Geometry utilizing the NCERT Exemplar Solutions will be able to comprehend the following:<\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">A line connecting two places has direction cosines and direction ratios. The shortest distance between two lines, coplanar and skew lines, and the Cartesian equation and vector equation of a line. A plane&#8217;s Cartesian and vector equations. The angle is formed by two lines, two planes, or a line and a plane. A point&#8217;s distance from a plane.<\/span><\/p>\n<p><span style=\"font-size: 14pt;\"><b>FAQ<\/b><\/span><\/p>\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=\"What_is_three_dimensional_geometry_in_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_11\"><\/span>What is three dimensional geometry in NCERT Exemplar Solutions for Class 12 Maths Chapter 11?<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\tIt is an area of mathematics that deals with three-dimensional coordinate systems and the study of lines, points, and solid objects. It will teach students how to use the z-coordinate in conjunction with the x and y coordinates to identify the precise location of a point in three-dimensional coordinate planes.\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=\"Is_NCERT_Exemplar_Solutions_for_Class_12_Maths_Chapter_11_the_best_study_material_for_the_students_during_revision\"><\/span>Is NCERT Exemplar Solutions for Class 12 Maths Chapter 11 the best study material for the students during revision?<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\tYes, the NCERT Exemplar Solutions for Class 12 Maths Chapter 11 is the finest study material for students who want to easily revise complicated ideas. Each solution includes a reasonable explanation to assist pupils in learning. INFINITY LEARN's in-house team of professionals has framed the step-by-step answers to encourage students to think analytically. These solutions can also be compared to obtain an idea of what different options are available for solving textbook problems.\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\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=\"What_are_the_important_topics_covered_in_Chapter_11_of_NCERT_Exemplar_Solutions_for_Class_12_Maths\"><\/span>What are the important topics covered in Chapter 11 of NCERT Exemplar Solutions for Class 12 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\tThe topics and subtopics covered in NCERT Exemplar Solutions for Class 12 Maths Chapter 11 are listed below: 11.1 Introduction 11.2 Direction Cosines and Direction Ratios of a Line 11.3 Equation of a Line in Space 11.4 Angle between Two Lines 11.5 Shortest Distance between Two Lines 11.6 Plane 11.7 Coplanarity of Two Lines 11.8 Angle between Two Planes 11.9 Distance of a Point from a Plane 11.10 Angle between a Line and a Plane.\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\": \"What is three dimensional geometry in NCERT Exemplar Solutions for Class 12 Maths Chapter 11?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"It is an area of mathematics that deals with three-dimensional coordinate systems and the study of lines, points, and solid objects. It will teach students how to use the z-coordinate in conjunction with the x and y coordinates to identify the precise location of a point in three-dimensional coordinate planes.\"\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\": \"Is NCERT Exemplar Solutions for Class 12 Maths Chapter 11 the best study material for the students during revision?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Yes, the NCERT Exemplar Solutions for Class 12 Maths Chapter 11 is the finest study material for students who want to easily revise complicated ideas. Each solution includes a reasonable explanation to assist pupils in learning. INFINITY LEARN's in-house team of professionals has framed the step-by-step answers to encourage students to think analytically. These solutions can also be compared to obtain an idea of what different options are available for solving textbook problems.\"\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\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the important topics covered in Chapter 11 of NCERT Exemplar Solutions for Class 12 Maths\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The topics and subtopics covered in NCERT Exemplar Solutions for Class 12 Maths Chapter 11 are listed below: 11.1 Introduction 11.2 Direction Cosines and Direction Ratios of a Line 11.3 Equation of a Line in Space 11.4 Angle between Two Lines 11.5 Shortest Distance between Two Lines 11.6 Plane 11.7 Coplanarity of Two Lines 11.8 Angle between Two Planes 11.9 Distance of a Point from a Plane 11.10 Angle between a Line and a Plane.\"\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<h3><span class=\"ez-toc-section\" id=\"Infinity_Learn_App\"><\/span><strong><span style=\"color: #0000ff;\">Infinity Learn App<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\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 12 Maths Chapter 11 Three Dimensional Geometry, which includes thorough solutions [&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 12 Maths Chapter 11","_yoast_wpseo_title":"NCERT Class 12 Maths Chapter 11 - Three Dimensional Geometry","_yoast_wpseo_metadesc":"Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry, which includes solutions.","custom_permalink":"study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/"},"categories":[106,109,105],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Class 12 Maths Chapter 11 - Three Dimensional Geometry<\/title>\n<meta name=\"description\" content=\"Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry, which includes solutions.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-12\/maths\/chapter-11-three-dimensional-geometry\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Class 12 Maths Chapter 11 - 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