{"id":32476,"date":"2022-03-30T10:00:12","date_gmt":"2022-03-30T04:30:12","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=32476"},"modified":"2022-03-30T10:05:22","modified_gmt":"2022-03-30T04:35:22","slug":"ncert-solutions-for-class-12-maths-chapter-10-ex-10-4","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-4\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 10 Vector Algebra Ex 10.4 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-4\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.4<\/h2>\n

\"NCERT<\/p>\n

Class 12 Maths Ex 10.4 Question 1.<\/strong>
\nFind \\(|\\vec{a} \\times \\vec{b}|\\), if \\(\\vec{a}=\\hat{i}-7 \\hat{j}+7 \\hat{k}\\) and \\(\\vec{b}=3 \\hat{i}-2 \\hat{j}+2 \\hat{k}\\).
\nSolution:
\n\"NCERT<\/p>\n

Question 2.
\nFind a unit vector perpendicular to each of the vector \\(\\overrightarrow { a } +\\overrightarrow { b } \\quad and\\quad \\overrightarrow { a } -\\overrightarrow { b } \\), where \\(\\overrightarrow { a } =3\\hat { i } +2\\hat { j } +2\\hat { k } \\quad and\\quad \\overrightarrow { b } =\\hat { i } +2\\hat { j } -2\\hat { k } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 3.
\nIf a unit vector \\(\\vec{a}\\) makes angles \\(\\frac { \u03c0 }{ 3 }\\) with \\(\\hat{i}\\), \\(\\frac { \u03c0 }{ 4 }\\) with \\(\\hat{j}\\) and an acute angle \u03b8 with k, then find \u03b8 and hence, the components of \\(\\vec{a}\\).
\nSolution:
\nThe direction cosines of \\(\\vec{a}\\) are
\n\"NCERT
\nSince \\(\\vec{a}\\) is a unit vector, its components are the direction cosines
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nShow that
\n\\((\\vec{a}-\\vec{b}) \\times(\\vec{a}+\\vec{b})=2(\\vec{a} \\times \\vec{b})\\)
\nSolution:
\n\\((\\vec{a}-\\vec{b}) \\times(\\vec{a}+\\vec{b})=\\vec{a} \\times \\vec{a}+\\vec{a} \\times \\vec{b}-\\vec{b} \\times \\vec{a}-\\vec{b} \\times \\vec{b}\\)
\n= \\(\\overrightarrow{0}+\\vec{a} \\times \\vec{b}+\\vec{a} \\times \\vec{b}-\\overrightarrow{0}\\)
\n= 2(\\(\\vec{a}\\) x \\(\\vec{b}\\))<\/p>\n

Question 5.
\nFind \u03bb and \u03bc if
\n\\(\\left( 2\\hat { i } +6\\hat { j } +27\\hat { k } \\right) \\times \\left( \\hat { i } +\\lambda \\hat { j } +\\mu \\hat { k } \\right)\\) = \\(\\vec{0}\\)
\nSolution:
\n\\((2 \\hat{i}+6 \\hat{j}+27 \\hat{k}) \\times(\\hat{i}+\\lambda \\hat{j}+\\mu \\hat{k})=\\overrightarrow{0}\\)
\n\\(\\left|\\begin{array}{ccc}
\n\\hat{i} & \\hat{j} & \\hat{k} \\\\
\n2 & 6 & 27 \\\\
\n1 & \\lambda & \\mu
\n\\end{array}\\right|=\\overrightarrow{0}\\)
\n\\(\\hat{i}(6 \\mu-27 \\lambda)-\\hat{j}(2 \\mu-27)+\\hat{k}(2 \\lambda-6)=\\overrightarrow{0}\\)
\nEquating the corresponding components, we get
\n6\u00b5 – 27\u03bb = 0 … (1)
\n– 2\u00b5 + 27 = 0 … (2)
\n2\u03bb – 6 = 0 … (3)
\n(2) \u2192 \u00b5 = \\(\\frac { 27 }{ 2 }\\), (3) \u2192 \u03bb = 3
\nSubstituting the values of \u03bb and \u00b5 in (1),
\nwe get 6(\\(\\frac { 27 }{ 2 }\\)) – 27(3) = 81 – 81 = 0
\n(1) satisfy \u03bb = 3 and \u00b5 = \\(\\frac { 27 }{ 2 }\\)
\nHence \u03bb = 3, \u00b5 = \\(\\frac { 27 }{ 2 }\\)<\/p>\n

Question 6.
\nGiven that \\(\\vec{a}\\).\\(\\vec{b}\\) = 0 and \\(\\vec{a}\\) x \\(\\vec{b}\\) = \\(\\vec{0}\\) What can you conclude about the vectors \\(\\vec{a}\\) and \\(\\vec{b}\\)?
\nSolution:
\n\\(\\vec{a}\\).\\(\\vec{b}\\) = 0 \u21d2 \\(\\vec{a}\\) = \\(\\vec{0}\\) or \\(\\vec{b}\\) = \\(\\vec{0}\\) or \\(\\vec{a}\\) \u22a5 \\(\\vec{b}\\)
\n\\(\\vec{a}\\) x \\(\\vec{b}\\) = \\(\\vec{0}\\) \u21d2 \\(\\vec{a}\\) = \\(\\vec{0}\\) or \\(\\vec{b}\\) = \\(\\vec{0}\\) or \\(\\vec{a}\\) || \\(\\vec{b}\\)
\nSince \\(\\vec{a}\\).\\(\\vec{b}\\) = 0 and \\(\\vec{a}\\) x \\(\\vec{b}\\) = 0,
\nthen either \\(\\vec{a}\\) = \\(\\vec{0}\\) or \\(\\vec{b}\\).\\(\\vec{0}\\)
\n\\(\\vec{a}\\) \u22a5 \\(\\vec{b}\\) and \\(\\vec{a}\\)||\\(\\vec{b}\\) are not possible at the same time.<\/p>\n

\"NCERT<\/p>\n

Question 7.
\nLet the vectors \\(\\vec{a}\\), \\(\\vec{b}\\), \\(\\vec{c}\\) be given as \\({ a }_{ 1 }\\hat { i } +{ a }_{ 2 }\\hat { j } +{ a }_{ 3 }\\hat { k } ,{ b }_{ 1 }\\hat { i } +{ b }_{ 2 }\\hat { j } +{ b }_{ 3 }\\hat { k } ,{ c }_{ 1 }\\hat { i } +{ c }_{ 2 }\\hat { j } +{ c }_{ 3 }\\hat { k }\\), then show that \\(\\vec{a} \\times(\\vec{b}+\\vec{c})=\\vec{a} \\times \\vec{b}+\\vec{a} \\times \\vec{c}\\).
\nSolution:
\n\"NCERT<\/p>\n

Question 8.
\nIf either \\(\\vec{a}=\\overrightarrow{0} \\text { or } \\vec{b}=\\overrightarrow{0} \\text {, then } \\vec{a} \\times \\vec{b}=\\overrightarrow{0}\\). Is the converse true? Justify your answer with an example.
\nSolution:
\n\\(\\vec{a} \\times \\vec{b}=|\\vec{a}||\\vec{b}| \\sin \\theta \\hat{n}\\)
\nIf \\(\\vec{a}=\\overrightarrow{0} \\text { or } \\vec{b}=\\overrightarrow{0} \\text {, then } \\vec{a} \\times \\vec{b}=\\overrightarrow{0}\\).
\nThe converse need not be true.
\nFor example, consider the non-zero parallel
\n\"NCERT<\/p>\n

Question 9.
\nFind the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).
\nSolution:
\n\"NCERT<\/p>\n

Question 10.
\nFind the area of the parallelogram whose adjacent sides are determined by the vectors \\(\\overrightarrow { a } =\\hat { i } -\\hat { j } +3\\hat { k } ,\\overrightarrow { b } =2\\hat { i } -7\\hat { j } +\\hat { k } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 11.
\nLet the vectors \\(\\vec{a}\\) and \\(\\vec{b}\\) such that |\\(\\vec{a}\\)| = 3 and |\\(\\vec{b}\\)| = \\(\\frac{\\sqrt{2}}{3}\\), then \\(\\vec{a}\\) x \\(\\vec{b}\\) is a unit vector if the angle between \\(\\vec{a}\\) and \\(\\vec{a}\\) is
\n(a) \\(\\frac { \\pi }{ 6 } \\)
\n(b) \\(\\frac { \\pi }{ 4 } \\)
\n(c) \\(\\frac { \\pi }{ 3 } \\)
\n(d) \\(\\frac { \\pi }{ 2 } \\)
\nSolution:
\nLet \u03b8 be the angle between vectors \\(\\vec{a}\\) and \\(\\vec{b}\\).
\nSince \\(\\vec{a}\\) x \\(\\vec{b}\\) is a unit vector,
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 12.
\nArea of a rectangles having vertices
\n\\(\\left( -\\hat { i } +\\frac { 1 }{ 2 } \\hat { j } +4\\hat { k } \\right), \\left( \\hat { i } +\\frac { 1 }{ 2 } \\hat { j } +4\\hat { k } \\right)\\)
\n\\(\\left( \\hat { i } -\\frac { 1 }{ 2 } \\hat { j } +4\\hat { k } \\right), \\left( -\\hat { i } -\\frac { 1 }{ 2 } \\hat { j } +4\\hat { k } \\right)\\)
\n(a) \\(\\frac { 1 }{ 2 }\\) sq units
\n(b) 1 sq.units
\n(c) 2 sq.units
\n(d) 4 sq.units
\nSolution:
\n\"NCERT<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-4\/ NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.4 Class 12 Maths Ex 10.4 Question 1. Find , if and . Solution: Question 2. Find a unit …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4<\/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 10.4 - 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-10-ex-10-4\/\" \/>\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 10 Vector Algebra Ex 10.4 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-4\/ NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.4 Class 12 Maths Ex 10.4 Question 1. 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