NCERT Solutions for Class 12 Maths<\/a> Chapter 10 Vector Algebra Ex 10.5 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-5\/<\/p>\nNCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.5<\/h2>\n <\/p>\n
Question 1. \nFind [a, b, c] if \\(\\vec{a}=\\hat{i}-2 \\hat{j}+3 \\hat{k}\\), \\(\\vec{b}=2 \\hat{i}-3 \\hat{j}+\\hat{k}\\) and \\(\\vec{c}=3 \\hat{i}+\\hat{j}-2 \\hat{k}\\) \nSolution: \n\\([\\vec{a}, \\vec{b}, \\vec{c}]=\\left|\\begin{array}{ccc} 1 & -2 & 3 \\\\ 2 & -3 & 1 \\\\ 3 & 1 & -2 \\end{array}\\right|\\) = 1(6 – 1)+2(- 4 – 3) + 3(2 + 9) = 1(5) + 2(- 7) + 3(11) = 24.<\/p>\n
Question 2. \nShow that the vectors \\(\\vec{a}=\\hat{i}-2 \\hat{j}+3 \\hat{k}\\), \\(\\vec{b}=-2 \\hat{i}+3 \\hat{j}-4\\hat{k}\\) and \\(\\vec{c}=\\hat{i}-3\\hat{j}+5 \\hat{k}\\) are coplanar. \nSolution: \n\\([\\vec{a}, \\vec{b}, \\vec{c}]=\\left|\\begin{array}{ccc} 1 & -2 & 3 \\\\ -2 & 3 & -4 \\\\ 1 & -3 & 5 \\end{array}\\right|\\) \n= 1(15 – 12)+2(- 10 + 4) + 3(6 – 3) \n= 1(3) + 2(- 6) + 3(3) = 0.<\/p>\n
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Question 3. \nFind \u03bb, if the vectors \\(\\hat{i}-\\hat{j}+\\hat{k}, 3 \\hat{i}+\\hat{j}+2 \\hat{k}\\) and \\(\\hat{i}+\\lambda \\hat{j}-3 \\hat{k}\\)are coplanar. \nSolution: \nLet \\(\\vec{a}=\\hat{i}-\\hat{j}+\\hat{k}\\), \\(\\vec{b}=3 \\hat{i}+\\hat{j}+2 \\hat{k}\\) and \\(\\vec{c}=\\hat{i}+\\lambda \\hat{j}-3 \\hat{k}\\) be the given vectors. \nSince the given vectors are coplanar \\([\\vec{a}, \\vec{b}, \\vec{c}]\\) = 0 \ni.e., \\(\\left|\\begin{array}{ccc} 1 & -1 & 1 \\\\ 3 & 1 & 2 \\\\ 1 & \\lambda & -3 \\end{array}\\right|\\) = 0 \n1(- 3 – 2\u03bb) + 1(- 9 – 2) + 1(3\u03bb – 1) = 0 \n– 3 – 2\u03bb – 11 + 3\u03bb – 1 = 0 \u21d2 \u03bb = 15<\/p>\n
Question 4. \ni. If c1<\/sub> = 1 and c2<\/sub> = 2, find c3<\/sub> which makes \\(\\vec{a}\\), \\(\\vec{b}\\) and \\(\\vec{c}\\) coplanar. \nii. Then if c2<\/sub> = – 1 and c3<\/sub> = 1, show that no value of c1<\/sub> can make \\(\\vec{a}\\), \\(\\vec{b}\\) and \\(\\vec{c}\\) coplanar. \nSolution: \ni. Given that \\(\\vec{a}\\), \\(\\vec{b}\\) and \\(\\vec{c}\\) are coplanar. \n\u2234 \\([\\vec{a}, \\vec{b}, \\vec{c}]\\) = 0 \n <\/p>\nQuestion 5. \nConsider the 4 points A, B, C and D with position vectors \\(4 \\hat{i}+8 \\hat{j}+12 \\hat{k}, 2 \\hat{i}+4 \\hat{j}+6 \\hat{k}\\) \\(3 \\hat{i}+5 \\hat{j}+4 \\hat{k} \\text { and } 5 \\hat{i}+8 \\hat{j}+5 \\hat{k}\\). \ni. Find \\(\\overrightarrow{\\mathrm{AB}}, \\overrightarrow{\\mathrm{AC}}, \\overrightarrow{\\mathrm{AD}}\\). \nii. Show that the 4 points are coplanar. \nSolution: \n <\/p>\n
Question 6. \nFind x such that the four points A(3, 2, 1), B(4, x, 5), C(4, 2, – 2) and D(6, 5, – 1) are coplanar \nSolution: \n <\/p>\n
ii. Since the 4 points A, B, C and D are coplanar \\([\\overrightarrow{\\mathrm{AB}}, \\overrightarrow{\\mathrm{AC}}, \\overrightarrow{\\mathrm{AD}}]\\) = 0 \n\\(\\left|\\begin{array}{ccc} \n1 & (x-2) & 4 \\\\ \n1 & 0 & -3 \\\\ \n3 & 3 & -2 \n\\end{array}\\right|\\) = 0 \n1(0 + 9) – (x – 2)(- 2+9) + 4(3 – 0) = 0 \n9 – 7(x – 2) + 12 = 0 \n9 – 7x + 14 + 12 = 0 \n\u21d2 7x = 35 \n\u2234 x = 5<\/p>\n
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Question 7. \nShow that the vectors \\(\\vec{a}\\), \\(\\vec{b}\\) and \\(\\vec{c}\\) are coplanar if \\(\\vec{a}\\) + \\(\\vec{b}\\), \\(\\vec{b}\\) + \\(\\vec{c}\\), \\(\\vec{c}\\) + \\(\\vec{a}\\) are coplanar. \nSolution: \n <\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.5 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-5\/ NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.5 Question 1. Find [a, b, c] if , and Solution: = 1(6 – 1)+2(- 4 – 3) + …<\/p>\n
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.5<\/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 10 Vector Algebra Ex 10.5 - 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