{"id":32405,"date":"2022-03-29T17:00:38","date_gmt":"2022-03-29T11:30:38","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=32405"},"modified":"2022-03-29T17:24:44","modified_gmt":"2022-03-29T11:54:44","slug":"ncert-solutions-for-class-12-maths-chapter-10-ex-10-2","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-2\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.2"},"content":{"rendered":"

These NCERT Solutions for Class 12 Maths<\/a> Chapter 10 Vector Algebra Ex 10.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-2\/<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.2<\/h2>\n

\"NCERT<\/p>\n

10.2 Class 12 Question 1.<\/strong>
\nCompute the magnitude of the following vectors:
\n\\(\\overrightarrow { a } =\\hat { i } +\\hat { j } +\\hat { k } ,\\overrightarrow { b } =\\hat { 2i } -\\hat { 7j } -\\hat { 3k } \\)
\n\\(\\overrightarrow { c } =\\frac { 1 }{ \\sqrt { 3 } } \\hat { i } +\\frac { 1 }{ \\sqrt { 3 } } \\hat { j } -\\frac { 1 }{ \\sqrt { 3 } } \\hat { k } \\)
\nSolution:
\n\"NCERT<\/p>\n

Question 2.
\nWrite two different vectors having same magnitude.
\nSolution:
\nLet \\(\\overrightarrow { a } =\\hat { i } +\\hat { 2j } +\\hat { 3k } ,\\overrightarrow { b } =\\hat { 3i } +\\hat { 2j } +\\hat { k } \\)
\n\\(|\\vec{a}|=\\sqrt{1+1+9}=\\sqrt{11}\\)
\n\\(|\\vec{b}|=\\sqrt{9+1+1}=\\sqrt{11}\\)
\n\u2234 \\(\\overline{a}\\) and \\(\\overline{b}\\) are examples for two vectors having the same magnitude.
\nThere are infinitely many Vectors having same magnitude.<\/p>\n

Question 3.
\nWrite two different vectors having same direction.
\nSolution:
\n\\(\\hat{i}+\\hat{j}+\\hat{k}\\) and \\(\\hat{3i}+\\hat{3j}+\\hat{3k}\\) are examples for two vectors having the same direction. Generally, if \\(\\vec{a}\\) is a nonzero vector, then \\(\\vec{a}\\) and \u03bb\\(\\vec{a}\\) have the same direction whenever \u03bb is positive.<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nFind the values of x and y so that the vectors \\(2 \\hat{i}+3 \\hat{j} \\text { and } x \\hat{i}+y \\hat{j}\\) are equal.
\nSolution:
\nWe are given \\(2 \\hat{i}+3 \\hat{j}=x \\hat{i}+y \\hat{j}\\)
\nIf vectors are equal, then their respective components are equal. Hence x = 2, y = 3.<\/p>\n

Question 5.
\nFind the scalar and vector components of the vector with initial point (2,1) and terminal point (-5,7).
\nSolution:
\nLet A(2, 1) be the initial point and B(-5,7) be the terminal point \\(\\overrightarrow { AB } =\\left( { x }_{ 2 }-{ x }_{ 1 } \\right) \\hat { i } +\\left( { y }_{ 2 }-{ y }_{ 1 } \\right) \\hat { j } =-\\hat { 7i } +\\hat { 6j } \\)
\n\u2234 The vector components are \\(\\vec{-7i}\\), \\(\\vec{6j}\\) and scalar components are – 7 and 6.<\/p>\n

Question 6.
\nFind the sum of three vectors:
\n\\(\\overrightarrow { a } =\\hat { i } -\\hat { 2j } +\\hat { k } ,\\overrightarrow { b } =-2\\hat { i } +\\hat { 4j } +5\\hat { k } \\quad and\\quad \\overrightarrow { c } =\\hat { i } -\\hat { 6j } -\\hat { 7k } ,\\)
\nSolution:
\n\\(\\overrightarrow { a } =\\hat { i } -\\hat { 2j } +\\hat { k } ,\\overrightarrow { b } =-2\\hat { i } +\\hat { 4j } +5\\hat { k } \\quad and\\quad \\overrightarrow { c } =\\hat { i } -\\hat { 6j } -\\hat { 7k }\\)<\/p>\n

Question 7.
\nFind the unit vector in the direction of the vector \\(\\overrightarrow { a } =\\hat { i } +\\hat { j } +\\hat { 2k } \\).
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 8.
\nFind the unit vector in the direction of vector \\(\\overrightarrow { PQ }\\), where P and Q are the points (1, 2, 3) and (4, 5, 6) respectively.
\nSolution:
\n\"NCERT<\/p>\n

Question 9.
\nFor given vectors \\(\\overrightarrow { a } =2\\hat { i } -\\hat { j } +2\\hat { k } \\quad and\\quad \\overrightarrow { b } =-\\hat { i } +\\hat { j } -\\hat { k }\\) find the unit vector in the direction of the vector \\(\\overrightarrow { a } +\\overrightarrow { b }\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 10.
\nFind a vector in the direction of \\(5\\hat { i } -\\hat { j } +2\\hat { k }\\) which has magnitude 8 units.
\nSolution:
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 11.
\nShow that the vector \\(2 \\hat{i}-3 \\hat{j}+4 \\hat{k}\\) and \\(-4 \\hat{i}+6 \\hat{j}-8 \\hat{k}\\) are collinear.
\nSolution:
\n\\(\\overrightarrow { a } =2\\hat { i } -3\\hat { j } +4\\hat { k } \\quad and\\quad \\overrightarrow { b } =-4\\hat { i } +6\\hat { j } -8\\hat { k } \\)
\n\\(=-2(2\\hat { i } -3\\hat { j } +4\\hat { k } ) \\)
\nvector \\(\\vec{a}\\) and \\(\\vec{b}\\) have the same direction they are collinear.<\/p>\n

Question 12.
\nFind the direction cosines of the vector \\(\\hat { i } +2\\hat { j } +3\\hat { k }\\)
\nSolution:
\n\"NCERT<\/p>\n

Question 13.
\nFind the direction cosines of the vector joining the points A (1, 2, – 3) and B(- 1, – 2, 1), directed from A to B.
\nSolution:
\n\"NCERT
\n\u2234 Direction cosines of \\(\\overline{AB}\\) = Scalar components of \\(\\overline{AB}\\)
\n= \\(\\frac{-1}{3}, \\frac{-2}{3}, \\frac{2}{3}\\)<\/p>\n

\"NCERT<\/p>\n

Question 14.
\nShow that the vector \\(\\hat { i } +\\hat { j } +\\hat { k }\\) are equally inclined to the axes OX, OY, OZ.
\nSolution:
\nLet \\(\\vec{r}\\) = \\(\\hat { i } +\\hat { j } +\\hat { k }\\)
\nThe direction ratios of \\(\\vec{r}\\) are 1, 1, 1.
\nThe direction cosines of \\(\\vec{r}\\) are
\n\\(\\frac{1}{\\sqrt{1^{2}+1^{2}+1^{2}}}, \\frac{1}{\\sqrt{1^{2}+1^{2}+1^{2}}}, \\frac{1}{\\sqrt{1^{2}+1^{2}+1^{2}}}\\)
\n\\(\\frac{1}{\\sqrt{3}}, \\frac{1}{\\sqrt{3}}, \\frac{1}{\\sqrt{3}}\\)
\n\u2234 \\(\\vec{r}\\) is equally inclined to the axes.<\/p>\n

Question 15.
\nFind the position vector of a point R which divides the line joining two points P and Q whose position vectors are \\(\\hat{i}+2 \\hat{j}-\\hat{k}\\) and \\(-\\hat{i}+\\hat{j}+\\hat{k}\\) respectively, in the ratio 2:1
\ni. internally
\nii. externally
\nSolution:
\ni. Internal division
\nLet \\(\\vec{a}\\) = position vectorof P = \\(\\hat{i}+2 \\hat{j}-\\hat{k}\\)
\nLet \\(\\vec{b}\\) = position vectorof Q = \\(-\\hat{i}+\\hat{j}+\\hat{k}\\)
\nLet R divides PQ internally in the ratio 2 : 1
\n\"NCERT<\/p>\n

ii. External division
\nLet S divides PQ externally in the ratio 2 : 1
\n\"NCERT<\/p>\n

Question 16.
\nFind position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, – 2).
\nSolution:
\nLet R be the midpoint of PQ
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 17.
\nShow that the points A, B and C with position vector \\(\\overrightarrow { a } =3\\hat { i } -4\\hat { j } -4\\hat { k } ,\\overrightarrow { b } =2\\hat { i } -\\hat { j } +\\hat { k } and\\quad \\overrightarrow { c } =\\hat { i } -3\\hat { j } -5\\hat { k }\\) respectively form the vertices of a right angled triangle.
\nSolution:
\n\"NCERT<\/p>\n

Question 18.
\nIn triangle ABC (fig.), which of the following is not
\n\"NCERT
\n(a) \\(\\overrightarrow { AB } +\\overrightarrow { BC } +\\overrightarrow { CA } =\\overrightarrow { 0 } \\)
\n(b) \\(\\overrightarrow { AB } +\\overrightarrow { BC } -\\overrightarrow { AC } =\\overrightarrow { 0 } \\)
\n(c) \\(\\overrightarrow { AB } +\\overrightarrow { BC } -\\overrightarrow { CA } =\\overrightarrow { 0 } \\)
\n(d) \\(\\overrightarrow { AB } -\\overrightarrow { CB } +\\overrightarrow { CA } =\\overrightarrow { 0 } \\)
\nSolution:
\nBy the triangle law of vector addition,
\n\\(\\overrightarrow { AB } +\\overrightarrow { BC } +\\overrightarrow { CA } =\\overrightarrow { 0 } \\)
\n\\(\\overrightarrow { AB } +\\overrightarrow { BC } -\\overrightarrow { AC } =\\overrightarrow { 0 } \\), is not true.<\/p>\n

\"NCERT<\/p>\n

Question 19.
\nIf \\(\\overrightarrow { a } ,\\overrightarrow { b } \\) are two collinear vectors then which of the following are incorrect:
\n(a) \\(\\overrightarrow { b } =\\lambda \\overrightarrow { a } \\), for some scalar \u03bb.
\n(b) \\(\\overrightarrow { a } =\\pm \\overrightarrow { b } \\)
\n(c) the respective components of \\(\\overrightarrow { a } ,\\overrightarrow { b } \\) are proportional.
\n(d) both the vectors \\(\\overrightarrow { a } ,\\overrightarrow { b } \\) have same direction, but different magnitudes.
\nSolution:
\nIf \\(\\vec{a}\\) and \\(\\vec{b}\\) are collinear, then they need not be in the same direction, d and b may have opposite directions.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-2\/ NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.2 10.2 Class 12 Question 1. Compute the magnitude of the following vectors: Solution: Question 2. Write two different …<\/p>\n

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.2<\/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 10.2 - 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-10-2\/\" \/>\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 10.2 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.2 Questions and Answers are prepared by our highly skilled subject experts. https:\/\/mcq-questions.com\/ncert-solutions-for-class-12-maths-chapter-10-ex-10-2\/ NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.2 10.2 Class 12 Question 1. 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