{"id":68042,"date":"2021-09-02T16:49:00","date_gmt":"2021-09-02T11:19:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68042"},"modified":"2021-09-02T16:49:32","modified_gmt":"2021-09-02T11:19:32","slug":"rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-15","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-15\/","title":{"rendered":"RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-123443\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-23-Exercise-23.15.jpg\" alt=\"RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-23-Exercise-23.15.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-23-Exercise-23.15-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15:\u00a0<\/strong>Students can use the solutions to self-analyze their shortcomings while solving problems from the RD Sharma textbook. The pdf of <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23\/\"><strong>RD Sharma Solutions Class 11 Maths Chapter 23<\/strong><\/a> Exercise 23.15 can be downloaded quickly from the links provided below and saved for future use.<\/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-69d331f072cb3\" 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-69d331f072cb3\"><\/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-23-exercise-23-15\/#download-rd-sharma-class-11-solutions-chapter-23-exercise-2315-free-pdf\" title=\"Download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15 Free PDF\">Download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15 Free PDF<\/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:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-15\/#access-answers-to-rd-sharma-solutions-class-11-maths-chapter-23-exercise-2315-important-question-with-answers\" title=\"Access answers to RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15- Important Question with Answers\">Access answers to RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15- Important Question with Answers<\/a><\/li><\/ul><\/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-23-exercise-23-15\/#faqs-on-rd-sharma-class-11-solutions-chapter-23-exercise-2315\" title=\"FAQs on RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15\">FAQs on RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15<\/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-23-exercise-23-15\/#where-can-i-download-rd-sharma-class-11-solutions-chapter-23-exercise-2315-free-pdf\" title=\"Where can I download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15 free PDF?\">Where can I download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15 free PDF?<\/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-23-exercise-23-15\/#why-is-kopykitab%e2%80%99s-rd-sharma-solutions-class-11-maths-chapter-23-exercise-2315-the-best-study-material\" title=\"Why is Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15 the best study material?\">Why is Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15 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-23-exercise-23-15\/#is-rd-sharma-solutions-for-class-12-maths-chapter-23-exercise-2315-for-free\" title=\"Is RD Sharma Solutions for Class 12 Maths Chapter 23 Exercise 23.15 for free?\">Is RD Sharma Solutions for Class 12 Maths Chapter 23 Exercise 23.15 for free?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-11-solutions-chapter-23-exercise-2315-free-pdf\"><\/span>Download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15 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-23-Ex-23.15-1.pdf\">RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15<\/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-23-Ex-23.15-1.pdf\", \"#example1\");<\/script><\/p>\n<p>Here, we&#8217;ll discuss about the concept of a point&#8217;s distance from a line. Students can easily get <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-rd-sharma-solutions\/\"><strong>RD Sharma Solutions for Class 11<\/strong><\/a> pdf to help them succeed in their board exams. After completing extensive research on each subject, the experienced faculty team at Kopykitab has solved and prepared answers for this exercise.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-11-maths-chapter-23-exercise-2315-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. Find the distance of the point (4, 5) from the straight line 3x \u2013 5y + 7 = 0.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7577\/16144332441_dc401a6e72_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-1\" width=\"390\" height=\"186\" \/><\/p>\n<p><strong>2. Find the perpendicular distance of the line joining the points (cos \u03b8, sin \u03b8) and (cos \u03d5, sin \u03d5) from the origin.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm9.staticflickr.com\/8570\/15960159089_76e03a1c23_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-12\" width=\"463\" height=\"607\" \/><\/p>\n<p><strong>3. Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are (a cos\u00a0\u03b1, a sin\u00a0\u03b1) and (a cos\u00a0\u03b2, a sin\u00a0\u03b2).<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7474\/16144332321_03054aab05_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-3\" width=\"682\" height=\"488\" \/><br \/><strong>Straight lines Ex 23.15 Q4<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7555\/15526512683_b40c1b578b_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-4\" width=\"632\" height=\"438\" \/><br \/><strong>Straight lines Ex 23.15 Q5<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7517\/15958795538_81e918ddea_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-5\" width=\"589\" height=\"383\" \/><br \/><strong>Straight lines Ex 23.15 Q6<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7562\/16120450576_16623bf81b_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-6\" width=\"494\" height=\"515\" \/><br \/><strong>Straight lines Ex 23.15 Q7<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7540\/15958795238_e9ea6cae8c_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-7\" width=\"521\" height=\"476\" \/><br \/><strong>Straight lines Ex 23.15 Q8<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7534\/15523903094_7b511e29b8_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-8\" width=\"534\" height=\"491\" \/><br \/><strong>Straight lines Ex 23.15 Q9<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8613\/15960159389_a65c018fc5_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-9\" width=\"429\" height=\"356\" \/><br \/><strong>Straight lines Ex 23.15 Q10<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7503\/15958795008_173c4dcd05_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-10\" width=\"558\" height=\"407\" \/><br \/><strong>Straight lines Ex 23.15 Q11<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7493\/15523902834_47c3d182a0_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-11\" width=\"520\" height=\"423\" \/><br \/><strong>Straight lines Ex 23.15 Q12<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7582\/15960158959_4d7044f298_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-13\" width=\"461\" height=\"260\" \/><br \/><strong>Straight lines Ex 23.15 Q13<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7476\/16146240025_40e4a3a76e_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-14\" width=\"522\" height=\"204\" \/><br \/><strong>Straight lines Ex 23.15 Q14<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7518\/15523902194_f68032d0e7_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-15\" width=\"594\" height=\"172\" \/><br \/><strong>Straight lines Ex 23.15 Q15<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7504\/15958934500_da970b018e_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-Straight-Lines-Ex-23.15-Q-2\" width=\"471\" height=\"299\" \/><\/p>\n<p>We have provided complete details of RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15. 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-23-exercise-2315\"><\/span>FAQs on RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15<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-1630580247979\" 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-23-exercise-2315-free-pdf\"><\/span>Where can I download RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15 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 for Class 11 Maths Chapter 23 Exercise 23.15 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630580465663\" 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-23-exercise-2315-the-best-study-material\"><\/span>Why is Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15 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 23 Exercise 23.15 available on Kopykitab\u2019s 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.\u00a0<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630580676992\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-rd-sharma-solutions-for-class-12-maths-chapter-23-exercise-2315-for-free\"><\/span>Is RD Sharma Solutions for Class 12 Maths Chapter 23 Exercise 23.15 for free?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, You can get RD Sharma Solutions Class 12 Maths Chapter 23 Exercise 23.15 for free.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15:\u00a0Students can use the solutions to self-analyze their shortcomings while solving problems from the RD Sharma textbook. The pdf of RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.15 can be downloaded quickly from the links provided below and saved for future use. Download RD &#8230; <a title=\"RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-15\/\" aria-label=\"More on RD Sharma Class 11 Solutions Chapter 23 Exercise 23.15 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":123443,"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\/68042"}],"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=68042"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68042\/revisions"}],"predecessor-version":[{"id":123665,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68042\/revisions\/123665"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/123443"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68042"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68042"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}