{"id":68079,"date":"2021-09-02T11:08:00","date_gmt":"2021-09-02T05:38:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68079"},"modified":"2021-09-02T12:39:15","modified_gmt":"2021-09-02T07:09:15","slug":"rd-sharma-solutions-class-11-maths-chapter-28-exercise-28-1","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-exercise-28-1\/","title":{"rendered":"RD Sharma Class 11 Solutions Chapter 28 Exercise 28.1 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-123127\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-28-Exercise-28.1.jpg\" alt=\"RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-28-Exercise-28.1.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-28-Exercise-28.1-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1:\u00a0<\/strong>We will cover concepts related to coordinates of a point in space, as well as signs of coordinates of a point, in this exercise. Students can utilise <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-rd-sharma-solutions\/\"><strong>RD Sharma Class 11 Solutions<\/strong><\/a> to help them get good grades on their board exams. The pdf of <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-introduction-to-3d-coordinate-geometry\/\"><strong>RD Sharma Solutions Class 11 Maths Chapter 28<\/strong><\/a> Exercise 28.1 is available in the links below, which can be readily downloaded and saved for future reference.<\/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-69d01d192d839\" 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\" 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-exercise-28-1\/#why-is-kopykitab%e2%80%99s-rd-sharma-solutions-class-11-maths-chapter-28-exercise-281-the-best-study-material\" title=\"Why is Kopykitab&#8217;s RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1 the best study material?\">Why is Kopykitab&#8217;s RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1 the best study material?<\/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-exercise-28-1\/#where-can-i-download-rd-sharma-class-11-solutions-chapter-28-exercise-281-free-pdf\" title=\"Where can I download RD Sharma Class 11 Solutions Chapter 28 Exercise 28.1 free PDF?\">Where can I download RD Sharma Class 11 Solutions Chapter 28 Exercise 28.1 free PDF?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-11-solutions-chapter-28-exercise-281-free-pdf\"><\/span>Download RD Sharma Class 11 Solutions Chapter 28 Exercise 28.1 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-28-Ex-28.1-1.pdf\">RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1<\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<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\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-28-Ex-28.1-1.pdf\", \"#example1\");<\/script><\/p>\n<p>Our expert teachers prepare the solutions in a step-by-step format to ensure that students properly understand the concepts.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-11-maths-chapter-28-exercise-281-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\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 XOYZ<\/p>\n<p><br \/><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 X\u2032OYZ<\/p>\n<p><br \/><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 XOY\u2032Z<\/p>\n<p><br \/><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 XOYZ\u2032<\/p>\n<p><br \/><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 X\u2032OY\u2032Z<\/p>\n<p><br \/><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 X\u2032OY\u2032Z\u2032<\/p>\n<p><br \/><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 XOY\u2032Z\u2032<\/p>\n<p><br \/><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 X\u2032OYZ\u2032<\/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 the yz-plane, a sign of its x-coordinate will change<\/p>\n<p>So, Image of point (-2, 3, 4) is\u00a0(2, 3, 4)<\/p>\n<p><br \/><strong>(ii)<\/strong>(-5, 4, -3)<\/p>\n<p>Since we need to find its image in the xz-plane, a sign of its y-coordinate will change<\/p>\n<p>So, Image of point (-5, 4, -3) is\u00a0(-5, -4, -3)<\/p>\n<p><br \/><strong>(iii)<\/strong>\u00a0(5, 2, -7)<\/p>\n<p>Since we need to find its image in the xy-plane, a sign of its z-coordinate will change<\/p>\n<p>So, Image of point (5, 2, -7) is\u00a0(5, 2, 7)<\/p>\n<p><br \/><strong>(iv)<\/strong>\u00a0(-5, 0, 3)<\/p>\n<p>Since we need to find its image in the xz-plane, a sign of its y-coordinate will change<\/p>\n<p>So, Image of point (-5, 0, 3) is\u00a0(-5, 0, 3)<\/p>\n<p><br \/><strong>(v)<\/strong>\u00a0(-4, 0, 0)<\/p>\n<p>Since we need to find its image in the xy-plane, a sign of its z-coordinate will change<\/p>\n<p>So, Image of point (-4, 0, 0) is\u00a0(-4, 0, 0)<\/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><img class=\"wp-image-123158 aligncenter\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/a-3.png\" alt=\"a\" width=\"501\" height=\"263\" \/><\/p>\n<p>Since the 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><br \/>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:\u00a0<\/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><br \/>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><br \/>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><br \/>A plane parallel to coordinate planes of x<sub>1<\/sub>\u00a0and x<sub>2<\/sub>\u00a0is yz-plane<\/p>\n<p><br \/>A plane parallel to coordinate planes of y<sub>1<\/sub>\u00a0and y<sub>2<\/sub>\u00a0is xz-plane<\/p>\n<p><br \/>A plane parallel to coordinate planes of z<sub>1<\/sub>\u00a0and z<sub>2<\/sub>\u00a0is xy-plane<\/p>\n<p><br \/>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><br \/>\u2234The edges of parallelepiped is 5, 5, 5<\/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:\u00a0<\/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><br \/>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><br \/>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><br \/>A plane parallel to coordinate planes of x<sub>1<\/sub>\u00a0and x<sub>2<\/sub>\u00a0is yz-plane<\/p>\n<p>A plane parallel to coordinate planes of y<sub>1<\/sub>\u00a0and y<sub>2<\/sub>\u00a0is xz-plane<\/p>\n<p><br \/>A plane parallel to coordinate planes of z<sub>1<\/sub>\u00a0and z<sub>2<\/sub>\u00a0is xy-plane<\/p>\n<p><br \/>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><br \/>\u2234The edges of parallelepiped is 2, 2, 3<\/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 of the point from the x-axis is given as:<\/p>\n<p><img class=\"alignnone  wp-image-123161\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/b-4.png\" alt=\"b\" width=\"139\" height=\"103\" \/><\/p>\n<p>The distance\u00a0of the point from y-axis is given as:<\/p>\n<p><img class=\"alignnone  wp-image-123162\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/c-3.png\" alt=\"c\" width=\"161\" height=\"96\" \/><\/p>\n<p>The distance\u00a0of the point from z-axis is given as:<\/p>\n<p><img class=\"alignnone  wp-image-123163\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/d-1.png\" alt=\"d\" width=\"146\" height=\"108\" \/><\/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:\u00a0<\/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>)<br \/><br \/>We need to make sure that the absolute value to be the same for all points.<\/p>\n<p>So let point A(3, -2, 5)<\/p>\n<p>The remaining 7 points are:<\/p>\n<p>Point B(3, 2, 5) (By changing the sign of y coordinate)<\/p>\n<p>Point C(-3, -2, 5) (By changing the sign of x coordinate)<\/p>\n<p>Point D(3, -2, -5) (By changing the sign of z coordinate)<\/p>\n<p>Point E(-3, 2, 5) (By changing the sign of x and y coordinate)<\/p>\n<p>Point F(3, 2, -5) (By changing the sign of y and z coordinate)<\/p>\n<p>Point G(-3, -2, -5) (By changing the sign of x and z coordinate)<\/p>\n<p>Point H(-3, 2, -5) (By changing the sign of x, y, and z coordinate)<\/p>\n<p>We have provided complete details of RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>\u00a0Class 11, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-11-solutions-chapter-28-exercise-281\"><\/span>FAQs on RD Sharma Class 11 Solutions Chapter 28 Exercise 28.1<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-1630566133551\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-questions-are-there-in-rd-sharma-solutions-class-11-maths-chapter-28-exercise-281\"><\/span>How many questions are there in RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are a total of 7 questions in RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630566189357\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"why-is-kopykitab%e2%80%99s-rd-sharma-solutions-class-11-maths-chapter-28-exercise-281-the-best-study-material\"><\/span>Why is Kopykitab&#8217;s RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1 the best study material?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1 available on Kopykitab&#8217;s website has been created by highly qualified experts to assist students in achieving high scores on the board exam. The solutions are well-organized and logical, giving pupils a clear picture of the most important questions. In the solutions, short tactics and ideas are emphasized to assist students in answering problems and saving time on the board exam.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630566300859\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-download-rd-sharma-class-11-solutions-chapter-28-exercise-281-free-pdf\"><\/span>Where can I download RD Sharma Class 11 Solutions Chapter 28 Exercise 28.1 free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 11 Maths Chapter 28 Exercise 28.1:\u00a0We will cover concepts related to coordinates of a point in space, as well as signs of coordinates of a point, in this exercise. Students can utilise RD Sharma Class 11 Solutions to help them get good grades on their board exams. The pdf of RD &#8230; <a title=\"RD Sharma Class 11 Solutions Chapter 28 Exercise 28.1 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-28-exercise-28-1\/\" aria-label=\"More on RD Sharma Class 11 Solutions Chapter 28 Exercise 28.1 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":123127,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3428,73334,73564,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68079"}],"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\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=68079"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68079\/revisions"}],"predecessor-version":[{"id":123215,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68079\/revisions\/123215"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/123127"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68079"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68079"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68079"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}