{"id":64050,"date":"2021-08-27T15:57:00","date_gmt":"2021-08-27T10:27:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=64050"},"modified":"2023-11-28T10:35:21","modified_gmt":"2023-11-28T05:05:21","slug":"rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/","title":{"rendered":"RD Sharma Solutions Class 11 Maths Chapter 28 &#8211; Introduction To 3D Coordinate Geometry (Updated For 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-121218\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/08\/RD-Sharma-Solutions-Class-11-Maths-Chapter-28-Introduction-To-3D-Coordinate-Geometry.jpg\" alt=\"RD Sharma Solutions Class 11 Maths Chapter 28 \" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/08\/RD-Sharma-Solutions-Class-11-Maths-Chapter-28-Introduction-To-3D-Coordinate-Geometry.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/08\/RD-Sharma-Solutions-Class-11-Maths-Chapter-28-Introduction-To-3D-Coordinate-Geometry-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 28<\/strong>:\u00a0So, to make it easier for you to understand the Chapter 28, you have RD Sharma Solutions for chapter 28 &#8211; Introduction to Coordinate Geometry. The <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-rd-sharma-solutions\/\" target=\"_blank\" rel=\"noopener noreferrer\">RD Sharma Class 11 Solutions<\/a> comprehensively present each topic. So, you get to know them better and be able to apply them when you solve the problems.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 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\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d00871d04c0\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" 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: #000000;color:#000000\" 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-69d00871d04c0\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-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:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#download-rd-sharma-solutions-class-11-maths-chapter-28-pdf\" title=\"Download RD Sharma Solutions Class 11 Maths Chapter 28 PDF\">Download RD Sharma Solutions Class 11 Maths Chapter 28 PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#exercise-wise-rd-sharma-solutions-class-11-maths-chapter-28\" title=\"Exercise-wise RD Sharma Solutions Class 11 Maths Chapter 28\">Exercise-wise RD Sharma Solutions Class 11 Maths Chapter 28<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#details-of-exercises-from-rd-sharma-solutions-class-11-maths-chapter-28\" title=\"Details of Exercises from RD Sharma Solutions Class 11 Maths Chapter 28\">Details of Exercises from RD Sharma Solutions Class 11 Maths Chapter 28<\/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:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#rd-sharma-class-11-chapter-28-exercise-281\" title=\"RD Sharma Class 11 Chapter 28 Exercise 28.1\">RD Sharma Class 11 Chapter 28 Exercise 28.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#rd-sharma-class-11-chapter-28-exercise-282\" title=\"RD Sharma Class 11 Chapter 28 Exercise 28.2\">RD Sharma Class 11 Chapter 28 Exercise 28.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#rd-sharma-class-11-chapter-28-exercise-283\" title=\"RD Sharma Class 11 Chapter 28 Exercise 28.3\">RD Sharma Class 11 Chapter 28 Exercise 28.3<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#access-rd-sharma-solutions-class-11-maths-chapter-28\" title=\"Access RD Sharma Solutions Class 11 Maths Chapter 28\u00a0\">Access RD Sharma Solutions Class 11 Maths Chapter 28\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#list-of-important-topics-from-rd-sharma-solutions-class-11-maths-chapter-28\" title=\"List of Important Topics from RD Sharma Solutions Class 11 Maths Chapter 28\">List of Important Topics from RD Sharma Solutions Class 11 Maths Chapter 28<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#rd-sharma-solutions-class-11-maths-chapter-28\" title=\"RD Sharma Solutions Class 11 Maths Chapter 28\">RD Sharma Solutions Class 11 Maths Chapter 28<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#faqs-on-rd-sharma-solutions-class-11-maths-chapter-28\" title=\"FAQs on RD Sharma Solutions Class 11 Maths Chapter 28\">FAQs on RD Sharma Solutions Class 11 Maths Chapter 28<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#are-the-solutions-rd-sharma-solutions-class-11-maths-chapter-28-relevant\" title=\"Are the solutions RD Sharma Solutions Class 11 Maths Chapter 28\u00a0relevant?\">Are the solutions RD Sharma Solutions Class 11 Maths Chapter 28\u00a0relevant?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#can-i-access-the-rd-sharma-solutions-class-11-maths-chapter-28-pdf-offline\" title=\"Can I access the RD Sharma Solutions Class 11 Maths Chapter 28\u00a0PDF offline?\">Can I access the RD Sharma Solutions Class 11 Maths Chapter 28\u00a0PDF offline?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/#how-much-does-it-cost-to-download-the-pdf-of-rd-sharma-solutions-class-11-maths-chapter-28\" title=\"How much does it cost to download the PDF of RD Sharma Solutions Class 11 Maths Chapter 28?\">How much does it cost to download the PDF of RD Sharma Solutions Class 11 Maths Chapter 28?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-11-maths-chapter-28-pdf\"><\/span><strong>Download RD Sharma Solutions Class 11 Maths Chapter 28 PDF<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/08\/rd-28.pdf\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 11 Maths Chapter 28<\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/08\/rd-28.pdf\",\"#example1\");<\/script><\/p>\n<h2><span class=\"ez-toc-section\" id=\"exercise-wise-rd-sharma-solutions-class-11-maths-chapter-28\"><\/span><strong>Exercise-wise RD Sharma Solutions Class 11 Maths Chapter 28<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-exercise-28-1\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Class 11 Chapter 28A<\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-exercise-28-2\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Class 11 Chapter 28B<\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-exercise-28-3\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Class 11 Chapter 28C<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"details-of-exercises-from-rd-sharma-solutions-class-11-maths-chapter-28\"><\/span><strong>Details of Exercises from RD Sharma Solutions Class 11 Maths Chapter 28<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Each exercise is related to a concept that you learn in the chapter, such as the coordinates of a point and its signs and the distance and section formulae. By going through the following sections, you will know the types of problems you have in each exercise. So, make sure to go through and solve them so that you score well in the exams.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"rd-sharma-class-11-chapter-28-exercise-281\"><\/span><strong>RD Sharma Class 11 Chapter 28 Exercise 28.1<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>There are seven questions in Exercise 28.1, and in each question, you will be given a set of coordinate points and asked to determine the distances between them. You may also have various three-dimensional figures for which you must estimate metrics such as area or the length of the sides or angles.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"rd-sharma-class-11-chapter-28-exercise-282\"><\/span><strong>RD Sharma Class 11 Chapter 28 <\/strong><strong>Exercise 28.2<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Exercise 28.2 has 12 questions. Here, it would help if you solved each of the 12 problems using the distance and section formulae.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"rd-sharma-class-11-chapter-28-exercise-283\"><\/span><strong>RD Sharma Class 11 Chapter 28 <\/strong><strong>Exercise 28.3<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In Exercise 28.3, you have a set of coordinate points using which you trace a three-dimensional figure. Once you do that, you determine the different metrics related to that three-dimensional figure using the distance and section formulae.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-class-11-maths-chapter-28\"><\/span>Access RD Sharma Solutions Class 11 Maths Chapter 28\u00a0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. Name the octants in which the following points lie:<br \/>(i) (5, 2, 3)<br \/>(ii) (-5, 4, 3)<br \/>(iii) (4, -3, 5)<br \/>(iv) (7, 4, -3)<br \/>(v) (-5, -4, 7)<br \/>(vi) (-5, -3, -2)<br \/>(vii) (2, -5, -7)<br \/>(viii) (-7, 2, -5)<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a0(5, 2, 3)<\/p>\n<p>In this case, since x, y and z all three are positive then octant will be\u00a0<em>XOYZ<\/em><\/p>\n<p><strong>(ii)<\/strong>\u00a0(-5, 4, 3)<\/p>\n<p>In this case, since x is negative and y and z are positive then the octant will be\u00a0<em>X\u2032OYZ<\/em><\/p>\n<p><strong>(iii)<\/strong>\u00a0(4, -3, 5)<\/p>\n<p>In this case, since y is negative and x and z are positive then the octant will be\u00a0<em>XOY\u2032Z<\/em><\/p>\n<p><strong>(iv)<\/strong>\u00a0(7, 4, -3)<\/p>\n<p>In this case, since z is negative and x and y are positive then the octant will be\u00a0<em>XOYZ\u2032<\/em><\/p>\n<p><strong>(v)<\/strong>\u00a0(-5, -4, 7)<\/p>\n<p>In this case, since x and y are negative and z is positive then the octant will be\u00a0<em>X\u2032OY\u2032Z<\/em><\/p>\n<p><strong>(vi)<\/strong>\u00a0(-5, -3, -2)<\/p>\n<p>In this case, since x, y and z all three are negative then octant will be\u00a0<em>X\u2032OY\u2032Z\u2032<\/em><\/p>\n<p><strong>(vii)<\/strong>\u00a0(2, -5, -7)<\/p>\n<p>In this case, since z and y are negative and x is positive then the octant will be\u00a0<em>XOY\u2032Z\u2032<\/em><\/p>\n<p><strong>(viii)<\/strong>\u00a0(-7, 2, -5)<\/p>\n<p>In this case, since x and z are negative and x is positive then the octant will be\u00a0<em>X\u2032OYZ\u2032<\/em><\/p>\n<p><strong>2. Find the image of:<br \/>(i) (-2, 3, 4) in the yz-plane<br \/>(ii) (-5, 4, -3) in the xz-plane<\/strong><\/p>\n<p><strong>(iii) (5, 2, -7) in the xy-plane<br \/>(iv) (-5, 0, 3) in the xz-plane<br \/>(v) (-4, 0, 0) in the xy-plane<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a0(-2, 3, 4)<\/p>\n<p>Since we need to find its image in yz-plane, a sign of its x-coordinate will change<\/p>\n<p><em>So, Image of point (-2, 3, 4) is\u00a0(2, 3, 4)<\/em><\/p>\n<p><strong>(ii)<\/strong>(-5, 4, -3)<\/p>\n<p>Since we need to find its image in xz-plane, sign of its y-coordinate will change<\/p>\n<p><em>So, Image of point (-5, 4, -3) is\u00a0(-5, -4, -3)<\/em><\/p>\n<p><strong>(iii)<\/strong>\u00a0(5, 2, -7)<\/p>\n<p>Since we need to find its image in xy-plane, a sign of its z-coordinate will change<\/p>\n<p><em>So, Image of point (5, 2, -7) is\u00a0(5, 2, 7)<\/em><\/p>\n<p><strong>(iv)<\/strong>\u00a0(-5, 0, 3)<\/p>\n<p>Since we need to find its image in xz-plane, sign of its y-coordinate will change<\/p>\n<p><em>So, Image of point (-5, 0, 3) is\u00a0(-5, 0, 3)<\/em><\/p>\n<p><strong>(v)<\/strong>\u00a0(-4, 0, 0)<\/p>\n<p>Since we need to find its image in xy-plane, sign of its z-coordinate will change<\/p>\n<p><em>So, Image of point (-4, 0, 0) is\u00a0(-4, 0, 0)<\/em><\/p>\n<p><strong>3. A cube of side 5 has one vertex at the point (1, 0, 1), and the three edges from this vertex are, respectively, parallel to the negative x and y-axes and positive z-axis. Find the coordinates of the other vertices of the cube.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:\u00a0A cube has side 4 having one vertex at (1, 0, 1)<\/p>\n<p>Side of cube = 5<\/p>\n<p>We need to find the coordinates of the other vertices of the cube.<\/p>\n<p>So let the Point A(1, 0, 1) and AB, AD and AE is parallel to \u2013ve x-axis, -ve y-axis and +ve z-axis respectively.<\/p>\n<p><strong><img class=\"\" title=\"Description: RD Sharma Solutions for Class 11 Maths Chapter 28 \u2013 image 1\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/description-rd-sharma-solutions-for-class-11-maths-chapter-28-image-1.png\" alt=\"Description: RD Sharma Solutions for Class 11 Maths Chapter 28 \u2013 image 1\" width=\"415\" height=\"218\" \/><\/strong><\/p>\n<p>Since side of cube = 5<\/p>\n<p>Point B is (-4, 0, 1)<\/p>\n<p>Point D is (1, -5, 1)<\/p>\n<p>Point E is (1, 0, 6)<\/p>\n<p>Now, EH is parallel to \u2013ve y-axis<\/p>\n<p>Point H is (1, -5, 6)<\/p>\n<p>HG is parallel to \u2013ve x-axis<\/p>\n<p>Point G is (-4, -5, 6)<\/p>\n<p>Now, again GC and GF is parallel to \u2013ve z-axis and +ve y-axis respectively<\/p>\n<p>Point C is (-4, -5, 1)<\/p>\n<p>Point F is (-4, 0, 6)<\/p>\n<p><strong>4. Planes are drawn parallel to the coordinates planes through the points (3, 0, -1) and (-2, 5, 4). Find the lengths of the edges of the parallelepiped so formed.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>Points are (3, 0, -1) and (-2, 5, 4)<\/p>\n<p>We need to find the lengths of the edges of the parallelepiped formed.<\/p>\n<p>For point (3, 0, -1)<\/p>\n<p>x<sub>1<\/sub>\u00a0= 3, y<sub>1<\/sub>\u00a0= 0 and z<sub>1<\/sub>\u00a0= -1<\/p>\n<p>For point (-2, 5, 4)<\/p>\n<p>x<sub>2<\/sub>\u00a0= -2, y<sub>2<\/sub>\u00a0= 5 and z<sub>2<\/sub>\u00a0= 4<\/p>\n<p>Plane parallel to coordinate planes of x<sub>1<\/sub>\u00a0and x<sub>2<\/sub>\u00a0is yz-plane<\/p>\n<p>Plane parallel to coordinate planes of y<sub>1<\/sub>\u00a0and y<sub>2<\/sub>\u00a0is xz-plane<\/p>\n<p>Plane parallel to coordinate planes of z<sub>1<\/sub>\u00a0and z<sub>2<\/sub>\u00a0is xy-plane<\/p>\n<p>Distance between planes x<sub>1<\/sub>\u00a0= 3 and x<sub>2<\/sub>\u00a0= -2 is 3 \u2013 (-2) = 3 + 2 = 5<\/p>\n<p>Distance between planes x<sub>1<\/sub>\u00a0= 0 and y<sub>2<\/sub>\u00a0= 5 is 5 \u2013 0 = 5<\/p>\n<p>Distance between planes z<sub>1<\/sub>\u00a0= -1 and z<sub>2<\/sub>\u00a0= 4 is 4 \u2013 (-1) = 4 + 1 = 5<\/p>\n<p><em>\u2234Theedges of parallelepiped is 5, 5, 5<\/em><\/p>\n<p><strong>5. Planes are drawn through the points (5, 0, 2) and (3, -2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelepiped so formed.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>Points are (5, 0, 2) and (3, -2, 5)<\/p>\n<p>We need to find the lengths of the edges of the parallelepiped formed<\/p>\n<p>For point (5, 0, 2)<\/p>\n<p>x<sub>1<\/sub>\u00a0= 5, y<sub>1<\/sub>\u00a0= 0 and z<sub>1<\/sub>\u00a0= 2<\/p>\n<p>For point (3, -2, 5)<\/p>\n<p>x<sub>2<\/sub>\u00a0= 3, y<sub>2<\/sub>\u00a0= -2 and z<sub>2<\/sub>\u00a0= 5<\/p>\n<p>Plane parallel to coordinate planes of x<sub>1<\/sub>\u00a0and x<sub>2<\/sub>\u00a0is yz-plane<\/p>\n<p>Plane parallel to coordinate planes of y<sub>1<\/sub>\u00a0and y<sub>2<\/sub>\u00a0is xz-plane<\/p>\n<p>Plane parallel to coordinate planes of z<sub>1<\/sub>\u00a0and z<sub>2<\/sub>\u00a0is xy-plane<\/p>\n<p>Distance between planes x<sub>1<\/sub>\u00a0= 5 and x<sub>2<\/sub>\u00a0= 3 is 5 \u2013 3 = 2<\/p>\n<p>Distance between planes x<sub>1<\/sub>\u00a0= 0 and y<sub>2<\/sub>\u00a0= -2 is 0 \u2013 (-2) = 0 + 2 = 2<\/p>\n<p>Distance between planes z<sub>1<\/sub>\u00a0= 2 and z<sub>2<\/sub>\u00a0= 5 is 5 \u2013 2 = 3<\/p>\n<p><em>\u2234Theedges of parallelepiped is 2, 2, 3<\/em><\/p>\n<p><strong>6. Find the distances of the point P (-4, 3, 5) from the coordinate axes.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>The point P (-4, 3, 5)<\/p>\n<p>The distance\u00a0of the point from x-axis is given as:<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 28\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-28-image-2.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 28 \u2013 image 2\" \/><\/p>\n<p>The distance\u00a0of the point from y-axis is given as:<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 28\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-28-image-3.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 28 \u2013 image 3\" \/><\/p>\n<p>The distance\u00a0of the point from z-axis is given as:<\/p>\n<p><img title=\"RD Sharma Solutions for Class 11 Maths Chapter 28\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/04\/rd-sharma-solutions-for-class-11-maths-chapter-28-image-4.png\" alt=\"RD Sharma Solutions for Class 11 Maths Chapter 28 \u2013 image 4\" \/><\/p>\n<p><strong>7. The coordinates of a point are (3, -2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given:<\/p>\n<p>Point (3, -2, 5)<\/p>\n<p>The Absolute value of any point(x, y, z) is given by,<\/p>\n<p>\u221a(x<sup>2<\/sup>\u00a0+ y<sup>2<\/sup>\u00a0+ z<sup>2<\/sup>)<\/p>\n<p>We need to make sure that the absolute value is the same for all points.<\/p>\n<p>So let the point A(3, -2, 5)<\/p>\n<p><em>The remaining 7 points are:<\/em><\/p>\n<p><em>Point B(3, 2, 5) (By changing the sign of y coordinate)<\/em><\/p>\n<p><em>Point C(-3, -2, 5) (By changing the sign of x coordinate)<\/em><\/p>\n<p><em>Point D(3, -2, -5) (By changing the sign of z coordinate)<\/em><\/p>\n<p><em>Point E(-3, 2, 5) (By changing the sign of x and y coordinate)<\/em><\/p>\n<p><em>Point F(3, 2, -5) (By changing the sign of y and z coordinate)<\/em><\/p>\n<p><em>Point G(-3, -2, -5) (By changing the sign of x and z coordinate)<\/em><\/p>\n<p><em>Point H(-3, 2, -5) (By changing the sign of x, y and z coordinate)<\/em><\/p>\n<h2><span class=\"ez-toc-section\" id=\"list-of-important-topics-from-rd-sharma-solutions-class-11-maths-chapter-28\"><\/span><strong>List of Important Topics from RD Sharma Solutions Class 11 Maths Chapter 28<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Chapter 28 in Maths for CBSE class 11 is essential, not only for the annual exams and the class 12 board exams but also for various other competitive exams, such as the Olympiads. The chapter also serves as a foundation for many higher-order topics that you will be studying later when you pursue courses like engineering or architecture.<\/p>\n<p>So, you must pay special attention to this chapter. In the following list, you will find those topics from chapter 28 that you need to focus on as they have appeared several times in the annual exams.<\/p>\n<ol>\n<li>Coordinates of a Point in Space<\/li>\n<li>Distance and Section Formulae<\/li>\n<\/ol>\n<p>The topics mentioned above form the core of the chapter. So, don\u2019t forget to go through and become thorough with them for you to write your exams.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-11-maths-chapter-28\"><\/span><strong>RD Sharma Solutions Class 11 Maths Chapter 28<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Chapter 28 in Maths for <a href=\"https:\/\/cbse.nic.in\/\" target=\"_blank\" rel=\"noopener noreferrer\">CBSE<\/a> class 11, \u2018Introduction to 3D Coordinate Geometry,\u2019 has various essential concepts for the exams. Many of these topics are also form the basis for other, higher-order concepts that you will be learning in courses like engineering.\u00a0<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-solutions-class-11-maths-chapter-28\"><\/span>FAQs on RD Sharma Solutions Class 11 Maths Chapter 28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630060155940\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"are-the-solutions-rd-sharma-solutions-class-11-maths-chapter-28-relevant\"><\/span>Are the solutions RD Sharma Solutions Class 11 Maths Chapter 28\u00a0relevant?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The solutions are relevant as they are designed by the subject matter experts. \u00a0<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630060241174\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-access-the-rd-sharma-solutions-class-11-maths-chapter-28-pdf-offline\"><\/span>Can I access the RD Sharma Solutions Class 11 Maths Chapter 28\u00a0PDF offline?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Once you have downloaded the PDF online, you can access it offline as well.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630060295862\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-much-does-it-cost-to-download-the-pdf-of-rd-sharma-solutions-class-11-maths-chapter-28\"><\/span>How much does it cost to download the PDF of RD Sharma Solutions Class 11 Maths Chapter 28?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download it for free.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 11 Maths Chapter 28:\u00a0So, to make it easier for you to understand the Chapter 28, you have RD Sharma Solutions for chapter 28 &#8211; Introduction to Coordinate Geometry. The RD Sharma Class 11 Solutions comprehensively present each topic. So, you get to know them better and be able to apply them &#8230; <a title=\"RD Sharma Solutions Class 11 Maths Chapter 28 &#8211; Introduction To 3D Coordinate Geometry (Updated For 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/\" aria-label=\"More on RD Sharma Solutions Class 11 Maths Chapter 28 &#8211; Introduction To 3D Coordinate Geometry (Updated For 2024)\">Read more<\/a><\/p>\n","protected":false},"author":243,"featured_media":121218,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3428,73334],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/64050"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/243"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=64050"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/64050\/revisions"}],"predecessor-version":[{"id":513208,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/64050\/revisions\/513208"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/121218"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=64050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=64050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=64050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}