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 <\/p>\nQuestion 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
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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 <\/p>\n
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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 <\/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 <\/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 <\/p>\n
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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 <\/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 \n\u2234 Direction cosines of \\(\\overline{AB}\\) = Scalar components of \\(\\overline{AB}\\) \n= \\(\\frac{-1}{3}, \\frac{-2}{3}, \\frac{2}{3}\\)<\/p>\n
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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 <\/p>\n
ii. External division \nLet S divides PQ externally in the ratio 2 : 1 \n <\/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 <\/p>\n
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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 <\/p>\n
Question 18. \nIn triangle ABC (fig.), which of the following is not \n \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
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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 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n