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