{"id":32555,"date":"2022-03-30T10:00:17","date_gmt":"2022-03-30T04:30:17","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=32555"},"modified":"2022-03-30T10:20:07","modified_gmt":"2022-03-30T04:50:07","slug":"ncert-solutions-for-class-12-maths-chapter-11-ex-11-1","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 11 Three Dimensional Geometry Ex 11.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11.1<\/h2>\n

\"NCERT<\/p>\n

Question 1.
\nIf a line makes angles 90\u00b0, 135\u00b0, 45\u00b0 with the x, y and z-axes respectively, find its direction cosines.
\nSolution:
\nLet the direction angles be \u03b1, \u00df, \u03b3.
\ni.e., \u03b1 = 90\u00b0, \u00df = 135\u00b0 and \u03b3 = 45\u00b0
\nThe direction cosines are cos \u03b1, cos \u00df, cos \u03b3 = cos 90\u00b0, cos 135\u00b0, cos45\u00b0
\n= 0, \\(\\frac{1}{\\sqrt{2}}, \\frac{1}{\\sqrt{2}}\\)<\/p>\n

Question 2.
\nFind the direction cosines of a line which makes equal angles with the coordinate axes.
\nSolution:
\nLet the direction angles be \u03b1, \u00df, \u03b3. Angles of the line. Since this makes equal angles with the axes, we get
\n\"NCERT<\/p>\n

Question 3.
\nIf a line has the direction ratios – 18, 12, – 4 then what are its direction cosines?
\nSolution:
\nThe direction ratios are – 18, 12, – 4
\n\\(\\sqrt{(-18)^{2}+(12)^{2}+(-4)^{2}}=\\sqrt{384}\\) = 22
\nThe direction cosines are
\n\\(\\frac{-18}{22}, \\frac{12}{22}, \\frac{-4}{22}=\\frac{-9}{11}, \\frac{6}{11}, \\frac{-2}{11}\\)<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nShow that the points (2, 3, 4) (- 1, – 2, 1), (5, 8, 7) are collinear.
\nSolution:
\nLet A (2, 3, 4), B (- 1, – 2, 1) and C (5, 8, 7) be the points.
\nDirection ratios of AB
\n= – 1 – 2, – 2 – 3, 1 – 4
\n= – 3, – 5, – 3
\nThe direction ratios of BC
\n= 5 + 1, 8 + 2, 7 – 1 = 6, 10, 6
\nThe direction ratios of AB and BC are proportional
\n\u2234 AB and BC are parallel.
\nHence A, B, C are collinear.<\/p>\n

Question 5.
\nFind the direction cosines of the sides of the triangle whose vertices are (3, 5, – 4), (- 1, 1, 2) and (- 5, – 5,- 2).
\nSolution:
\nLet A (3, 5, – 4) B (- 1, 1, 2) and C (- 5, – 5, – 2) are the vertices of \u2206ABC
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/ NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11.1 Question 1. If a line makes angles 90\u00b0, 135\u00b0, 45\u00b0 with the x, y and z-axes …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[3],"tags":[],"yoast_head":"\nNCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/ NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11.1 Question 1. If a line makes angles 90\u00b0, 135\u00b0, 45\u00b0 with the x, y and z-axes … NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ Questions\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-30T04:30:17+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-30T04:50:07+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:site\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mcq-questions.com\/#website\",\"url\":\"https:\/\/mcq-questions.com\/\",\"name\":\"MCQ Questions\",\"description\":\"MCQ Questions for Class 1 to 12\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mcq-questions.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"contentUrl\":\"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1\",\"width\":170,\"height\":17,\"caption\":\"NCERT Solutions\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#webpage\",\"url\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/\",\"name\":\"NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 - MCQ Questions\",\"isPartOf\":{\"@id\":\"https:\/\/mcq-questions.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#primaryimage\"},\"datePublished\":\"2022-03-30T04:30:17+00:00\",\"dateModified\":\"2022-03-30T04:50:07+00:00\",\"author\":{\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\"},\"breadcrumb\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mcq-questions.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1\"}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/mcq-questions.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 - MCQ Questions","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 - MCQ Questions","og_description":"These NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/ NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11.1 Question 1. If a line makes angles 90\u00b0, 135\u00b0, 45\u00b0 with the x, y and z-axes … NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 Read More »","og_url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/","og_site_name":"MCQ Questions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2022-03-30T04:30:17+00:00","article_modified_time":"2022-03-30T04:50:07+00:00","og_image":[{"url":"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/mcq-questions.com\/#website","url":"https:\/\/mcq-questions.com\/","name":"MCQ Questions","description":"MCQ Questions for Class 1 to 12","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mcq-questions.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","contentUrl":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","width":170,"height":17,"caption":"NCERT Solutions"},{"@type":"WebPage","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#webpage","url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/","name":"NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1 - MCQ Questions","isPartOf":{"@id":"https:\/\/mcq-questions.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#primaryimage"},"datePublished":"2022-03-30T04:30:17+00:00","dateModified":"2022-03-30T04:50:07+00:00","author":{"@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3"},"breadcrumb":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-11-ex-11-1\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mcq-questions.com\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.1"}]},{"@type":"Person","@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/mcq-questions.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32555"}],"collection":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/comments?post=32555"}],"version-history":[{"count":2,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32555\/revisions"}],"predecessor-version":[{"id":37799,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/32555\/revisions\/37799"}],"wp:attachment":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/media?parent=32555"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/categories?post=32555"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/tags?post=32555"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}