{"id":21223,"date":"2020-01-24T15:37:41","date_gmt":"2020-01-24T10:07:41","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=21223"},"modified":"2021-07-02T15:27:05","modified_gmt":"2021-07-02T09:57:05","slug":"2nd-puc-maths-question-bank-chapter-10-miscellaneous-ex","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-maths-question-bank-chapter-10-miscellaneous-ex\/","title":{"rendered":"2nd PUC Maths Question Bank Chapter 10 Vector Algebra Miscellaneous Exercise"},"content":{"rendered":"

Students can Download Maths Chapter 10 Vector Algebra Miscellaneous Exercise Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers<\/a>\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 2nd PUC Maths Question Bank Chapter 10 Vector Algebra Miscellaneous Exercise<\/h2>\n

Question 1.
\nWrite down a unit vector in XY-plane, making an angle of 30\u00b0 with the positive direction of x-axis.
\nAnswer:
\nLet OP be the required vector
\n\"2nd<\/p>\n

Question 2.
\nFind the scalar components and magnitude of the vector joining the points P(x1,<\/sub>y1<\/sub>,z1<\/sub>) and Q (x2<\/sub>, y2<\/sub>, z2<\/sub>).
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nA girl walks 4 km towards west, then she walks 3 km in a direction 30\u00b0 east of north and stops. Determine the girl\u2019s displacement from her initial point of departure.
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 4.
\n\\(\\overrightarrow{\\mathbf{a}}=\\overrightarrow{\\mathbf{b}}+\\overrightarrow{\\mathbf{c}}, \\text { then is it true that }|\\overrightarrow{\\mathbf{a}}|=|\\overrightarrow{\\mathbf{b}}|+|\\overrightarrow{\\mathbf{c}}|\\) justify your answer.
\nAnswer:
\n\"2nd<\/p>\n

Question 5.
\nFind the value of x for which \\(\\mathbf{x}(\\hat{\\mathbf{i}}+\\hat{\\mathbf{j}}+\\hat{\\mathbf{k}}) \\)is a unit vector.
\nAnswer:
\n\"2nd<\/p>\n

Question 6.
\nFind a vector of magnitude 5 units, and parallel to the resultant of the vectors
\n\\(\\overrightarrow{\\mathrm{a}}=2 \\hat{\\mathrm{i}}+3 \\hat{\\mathrm{j}}-\\hat{\\mathrm{k}} \\text { and } \\overrightarrow{\\mathrm{b}}=\\hat{\\mathrm{i}}-2 \\hat{\\mathrm{j}}+\\hat{\\mathrm{k}}\\)
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 7.
\nIf\\(\\overrightarrow{\\mathrm{a}}=\\hat{\\mathbf{i}}+\\hat{\\mathbf{j}}+\\hat{\\mathbf{k}}, \\overrightarrow{\\mathbf{b}}=2 \\hat{\\mathbf{i}}-\\hat{\\mathbf{j}}+3 \\hat{\\mathbf{k}} \\text { and }\\) and \\(\\overrightarrow{\\mathbf{c}}=\\hat{\\mathbf{i}}-2 \\hat{\\mathbf{j}}+\\hat{\\mathbf{k}}\\)find a unit vector parellel to the vector
\n\\(2 \\vec{a}-\\vec{b}+3 \\vec{c}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 8.
\nShow that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
\nAnswer:
\n\"2nd
\n\u2234 hence AC and AB are coimear. Since A s
\ncommon A, B, C arc collinear
\nLet B divide AC in the ratio k: I
\n\"2nd<\/p>\n

Question 9.
\nFind the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2a + b) and \\((\\vec{a}-3 \\vec{b})\\)externally in the ratio 1:2. Also, show that P is the mid point of the line segment RQ.
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 10.
\nThe two adjacent sides of a parallelogram are \\(2 \\hat{\\mathbf{i}}-4 \\hat{\\mathbf{j}}+5 \\hat{\\mathbf{k}} \\text { and } \\hat{\\mathbf{i}}-2 \\hat{\\mathbf{j}}-3 \\hat{\\mathbf{k}}\\) .Find the unit vector parallel to its diagonal. Also,find its area.
\nAnswer:
\n\"2nd<\/p>\n

Question 11.
\nShow that the direction cosines of a vector equally inclined to the axes OX, OY and OZ
\n\\(\\frac{1}{\\sqrt{3}}, \\frac{1}{\\sqrt{3}}, \\frac{1}{\\sqrt{3}}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 12.
\nLet \\(\\overrightarrow{\\mathrm{a}}=\\hat{\\mathbf{i}}+4 \\hat{\\mathbf{j}}+2 \\hat{\\mathbf{k}}, \\overrightarrow{\\mathbf{b}}=3 \\hat{\\mathbf{i}}-2 \\hat{\\mathbf{j}}+7 \\hat{\\mathbf{k}} \\text { and }\\overrightarrow{\\mathrm{c}}=2 \\hat{\\mathrm{i}}-\\hat{\\mathrm{j}}+4 \\hat{\\mathrm{k}}\\) .find the vector \\(\\overrightarrow{\\mathrm{d}}\\) which is perpendicular to both \\(\\overrightarrow{\\mathbf{a}} \\text { and } \\overrightarrow{\\mathbf{b}} \\text { and } \\overrightarrow{\\mathbf{c}} . \\overrightarrow{\\mathbf{d}}\\) = 15
\nAnswer:
\n\"2nd<\/p>\n

Question 13.
\nThe scalar product of the vector \\(\\hat{\\mathbf{i}}+\\hat{\\mathbf{j}}+\\hat{\\mathbf{k}}\\) a unit vector along the sum of vectors \\(2 \\hat{\\mathbf{i}}+4 \\hat{\\mathbf{j}}-5 \\hat{\\mathbf{k}} \\text { and } \\quad \\lambda \\hat{\\mathbf{i}}+2 \\hat{\\mathbf{j}}+3 \\hat{\\mathbf{k}}\\) is equal to ane. find the value of \u03bb.
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 14.
\nIf \\(\\overrightarrow{\\mathbf{a}}, \\overrightarrow{\\mathbf{b}}, \\overrightarrow{\\mathbf{c}}\\) are mutually perpendicular vectors of equal magnitudes, show that the vector is equally inclined to \\(\\overrightarrow{\\mathbf{a}}, \\overrightarrow{\\mathbf{b}}, \\overrightarrow{\\mathbf{c}}\\)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 15.
\nProve that
\n\\((\\overrightarrow{\\mathbf{a}}+\\overrightarrow{\\mathbf{b}}) \\cdot(\\overrightarrow{\\mathbf{a}}+\\overrightarrow{\\mathbf{b}})=|\\overrightarrow{\\mathbf{a}}|^{2}+|\\overrightarrow{\\mathbf{b}}|^{2}\\) if and only if \\(\\overrightarrow{\\mathbf{a}}, \\overrightarrow{\\mathbf{b}}\\) are perpendicular ,givens \\(\\overrightarrow{\\mathrm{a}} \\neq \\overrightarrow{0}, \\overrightarrow{\\mathrm{b}} \\neq \\overrightarrow{0}\\)
\nAnswer:
\n\"2nd<\/p>\n

Choose the correct answer in Exercises 16 to 19.<\/p>\n

Question 16.
\nIf \u03b8 is the angle between two vectors \\(\\overrightarrow { { a } } \\) and \\(\\overrightarrow { { b } } \\), then 3.6 > 0 only when then \\(\\overrightarrow{\\mathbf{a}} \\cdot \\overrightarrow{\\mathbf{b}} \\geq \\mathbf{0}\\) only when
\n(A)\\(0<\\theta<\\frac{\\pi}{2}\\)
\n(B)\\(0 \\leq \\theta \\leq \\frac{\\pi}{2}\\)
\n(C) 0<\u03b8<\u03c0
\n(D) 0\u2264\u03b8\u2264\u03c0
\nAnswer:
\n\"2nd<\/p>\n

Question 17.
\nlet \\(\\overrightarrow{\\mathbf{a}} \\text { and } \\overrightarrow{\\mathbf{b}}\\) be two unit vector and \u03b8 is the angle between them. Then 3 + b is a unit vector if
\n\"2nd
\nAnswer:
\n\"2nd<\/p>\n

Question 18.
\nThe value\\(\\hat{\\mathbf{i}} \\cdot(\\hat{\\mathbf{j}} \\times \\hat{\\mathbf{k}})+\\hat{\\mathbf{j}} \\cdot(\\hat{\\mathbf{i}} \\times \\hat{\\mathbf{k}})+\\hat{\\mathbf{k}} \\cdot(\\hat{\\mathbf{i}} \\times \\hat{\\mathbf{j}})\\)
\n(A) 0
\n(B) -1
\n(C) 1
\n(D) 3
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 19.
\nIf \u03b8 is the angle between any two vectors \\(\\overrightarrow{\\mathbf{a}} \\text { and } \\overrightarrow{\\mathbf{b}}, \\text { then }|\\overrightarrow{\\mathbf{a}} \\cdot \\overrightarrow{\\mathbf{b}}|=|\\overrightarrow{\\mathbf{a}} \\times \\overrightarrow{\\mathbf{b}}| \\)when \u03b8 is equal to
\n(A) 0
\n(B) \\(\\frac{\\pi}{4}\\)
\n(C) \\(\\frac{\\pi}{2}\\)
\n(D) \u03c0
\nAnswer:
\n\"2nd<\/p>\n

2nd PUC Maths Vector Algebra Miscellaneous Exercise Extra Questions and Answers<\/h3>\n

Question 1.
\nWrite a vector of magnitude 9 units in the direction of vector \\(-2 \\hat{\\mathbf{i}}+\\hat{\\mathbf{j}}+2 \\hat{\\mathbf{k}}\\) (CBSE 2019)
\nAnswer:
\n\"2nd<\/p>\n

Question 2.
\nfind
\n\\(\\lambda \\text { if }(2 i+6 j+4 k) \\times(i-\\lambda j+7 k)=0\\)(CBSE 2010)
\nAnswer:
\n\"2nd<\/p>\n

Question 3.
\nIf \\(\\overline{\\mathbf{a}} \\text { and } \\overline{\\mathbf{b}}\\) are two vectors such that \\(|\\overline{\\mathbf{a}} \\cdot \\overline{\\mathbf{b}}|=|\\overline{\\mathbf{a}} \\times \\overline{\\mathbf{b}}|\\), what is the angle between \\(\\overline{\\mathbf{a}} \\text { and } \\overline{\\mathbf{b}}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 4.
\n\\(|\\vec{a}|=\\sqrt{3},|\\vec{b}|=\\frac{2}{3} \\text { and } \\vec{a} \\times \\vec{b}\\)
\nis a vunit vector. Write the angle between \\(\\overline{\\mathbf{a}} \\text { and } \\overline{\\mathbf{b}}\\) (CBSE 2010)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 5.
\nWrite the projection of i – j on i + j (CBSE 2011)
\nAnswer:
\n\"2nd<\/p>\n

Question 6.
\nWrite the value of \\((\\mathbf{i} \\times \\mathbf{j}) \\cdot \\overline{\\mathbf{k}}+\\mathbf{i} \\cdot \\mathbf{j}\\)(CBSE 2012)
\nAnswer:
\n\"2nd<\/p>\n

Question 7.
\nFind the scalar components of the vector \\(\\overrightarrow{\\mathbf{A B}}\\)\u00a0with initial point A (2,1) and terminal point (-5,7).\u00a0\u00a0\u00a0\u00a0 (CBSE 2012)
\nAnswer:
\n\"2nd<\/p>\n

Question 8.
\n\\(\\bar { a } =\\vec { i } +4\\vec { j } +2\\vec { k } ,\\quad \\bar { b } =3\\vec { i } -2\\vec { j } +7\\bar { k } ,\\bar { c } =3\\vec { i } -\\vec { j } +4\\bar { k } \\) .find a vector \\(\\overline{\\mathbf{p}}\\) which is perpendicular both \\(\\overline{\\mathbf{a}} \\text { and } \\overline{\\mathbf{b}} \\text { and } \\overline{\\mathbf{p}} . \\overline{\\mathbf{c}}=18\\)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 9.
\nIf \\(\\overline { { a } } =\\overrightarrow { { i } } +\\overrightarrow { { j } } +\\overline { { k } } ,\\quad \\overline { { b } } =4\\overrightarrow { { i } } -2\\overrightarrow { { j } } +3\\overline { { k } } ,\\overline { { c } } =\\overrightarrow { { i } } -2\\overrightarrow { { j } } +\\overline { { k } } \\),find a vector of magnitude 6 units which is parallel to the vector \\(2\\overline { { a } } -\\overline { b } +\\overline { { 3c } } \\)
\nAnswer:
\n\"2nd<\/p>\n

Question 10.
\n\\(\\overline { { a } } =\\overrightarrow { { i } } +4\\overrightarrow { { j } } +2\\overline { { k } } ,\\quad \\overline { { b } } =3\\overrightarrow { { i } } -2\\overrightarrow { { j } } +7\\overline { { k } } ,\\overline { { c } } =2\\overrightarrow { { i } } -\\overrightarrow { { j } } +4\\overline { { k } } \\). find a vector d such that it is perpendiular to both \\(\\overline{\\mathbf{a}} \\text { and } \\overline{\\mathbf{b}} \\text { and }\\overrightarrow{\\mathrm{c}} \\cdot \\overrightarrow{\\mathrm{d}}=18\\)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 11.
\nUsing vectors find the area of the triangle with vectors A (1, 1, 2) , B (2, 3, 5), C(1, 5, 5) .\u00a0\u00a0 (CBSE 2011)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 12.
\n\\(\\alpha=3 i – j, \\bar{\\beta}=2 i+j-3 \\bar{k}\\) Express \u03b2 in the form the form
\n\u03b2 = \u03b21 <\/sub>+ \u03b22<\/sub> where \u03b21<\/sub>|| \u03b1 and \u03b22<\/sub> \u22a5\u03b1 (CBSE 2012)
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 13.
\n\\(\\begin{aligned}&\\overline{\\mathbf{a}} \\times \\overline{\\mathbf{b}}=\\overline{\\mathbf{c}} \\times \\overline{\\mathbf{d}}, \\quad \\overline{\\mathbf{a}} \\times \\overline{\\mathbf{c}}=\\overline{\\mathbf{b}} \\times \\overline{\\mathbf{d}} \\text { Show that }\\\\&(\\overline{\\mathbf{a}}-\\overline{\\mathbf{d}}) \\| \\mathbf{t} \\mathbf{o}-\\overline{\\mathbf{c}} \\text { when } \\overline{\\mathbf{a}} \\neq \\overline{\\mathbf{d}} \\text { and } \\overline{\\mathbf{b}} \\neq \\overline{\\mathbf{c}}\\end{aligned}\\)(ISE 2011)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 14.
\nfind
\n\\(\\overline{\\mathbf{a}} \\cdot \\overline{\\mathbf{b}} \\text { of }|\\overline{\\mathbf{a}}|=\\mathbf{3},|\\overline{\\mathbf{b}}|=\\mathbf{4},|\\overline{\\mathbf{a}} \\times \\mathbf{b}|=6\\) (CBSE 2009)
\nAnswer:
\n\"2nd<\/p>\n

Question 15.
\nIf \\(\\overline{\\mathbf{a}}, \\overline{\\mathbf{b}}, \\overline{\\mathbf{c}}\\) represent the sides of \u0394 show that \\(\\overline{\\mathbf{a}} \\times \\overline{\\mathbf{b}}=\\overline{\\mathbf{b}} \\times \\overline{\\mathbf{c}}=\\overline{\\mathbf{c}} \\times \\overline{\\mathbf{a}}\\) hence derive sine formula. (CBSE 2008)
\nAnswer:
\n\"2nd<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 10 Vector Algebra Miscellaneous Exercise Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Maths Question Bank Chapter 10 Vector Algebra Miscellaneous Exercise Question 1. Write down a …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21223"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=21223"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21223\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=21223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=21223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=21223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}