{"id":21141,"date":"2020-01-23T17:53:16","date_gmt":"2020-01-23T12:23:16","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=21141"},"modified":"2021-07-02T15:27:08","modified_gmt":"2021-07-02T09:57:08","slug":"2nd-puc-maths-question-bank-chapter-10-ex-10-3","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-maths-question-bank-chapter-10-ex-10-3\/","title":{"rendered":"2nd PUC Maths Question Bank Chapter 10 Vector Algebra Ex 10.3"},"content":{"rendered":"

Students can Download Maths Chapter 10 Vector Algebra Ex 10.3 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 Ex 10.3<\/h2>\n

2nd PUC Maths Vector Algebra NCERT Text Book Questions and Answers Ex 10.3<\/h3>\n

Question 1.
\nFind the angle between two vectors \\(\\overrightarrow{\\mathbf{a}} \\text { and } \\overrightarrow{\\mathbf{b}}\\) with magnitudes \\(\\sqrt{3}\\) and 2 respectively having \\(\\overrightarrow{\\mathrm{a}} \\cdot \\overrightarrow{\\mathrm{b}}=\\sqrt{6}\\)
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 2.
\nFind the angle between the vectors
\n\\(\\hat{\\mathbf{i}}-2 \\hat{\\mathbf{j}}+3 \\hat{\\mathbf{k}} \\text { and } 3 \\hat{\\mathbf{i}}-2 \\hat{\\mathbf{j}}+\\hat{\\mathbf{k}}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 3.
\nFind the projection of the vector \\(\\hat{\\mathbf{i}}-\\hat{\\mathbf{j}}\\) on the vector \\(\\hat{\\mathbf{i}}+\\hat{\\mathbf{j}}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 4.
\nFind the projection of the vector \\(\\hat{\\mathbf{i}}+3 \\hat{\\mathbf{j}}+7 \\hat{\\mathbf{k}}\\) on the vector \\(7 \\hat{\\mathbf{i}}-\\hat{\\mathbf{j}}+8 \\hat{\\mathbf{k}}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 5.
\nShow that each of the given three vectors is a unit vector.
\n\\(\\frac{1}{7}(2 \\hat{i}+3 \\hat{j}+6 \\hat{k}), \\frac{1}{7}(3 \\hat{i}-6 \\hat{j}+2 \\hat{k}), \\frac{1}{7}(6 \\hat{i}+2 \\hat{j}-3 \\hat{k})\\)
\nAlso, show that they are mutually perpendicular to each other.
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 6.
\n\\(\\text { Find }|\\overrightarrow{\\mathrm{a}}| \\text { and }|\\overrightarrow{\\mathrm{b}}|, \\text { if }(\\overrightarrow{\\mathrm{a}}+\\overrightarrow{\\mathrm{b}}) \\cdot(\\overrightarrow{\\mathrm{a}}-\\overrightarrow{\\mathrm{b}})=8 \\text { and }|\\overrightarrow{\\mathrm{a}}|=8|\\overrightarrow{\\mathrm{b}}|\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 7.
\nEvaluate the product
\n\\((3 \\vec{a}-5 \\vec{b}) \\cdot(2 \\vec{a}+7 \\vec{b})\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 8.
\nFind the magnitude of two vectors \\(\\overrightarrow{\\mathbf{a}} \\text { and } \\overrightarrow{\\mathbf{b}}\\), having the same magnitude and such that the angle between them is 60\u00b0 and their scalar product is 1\/2
\nAnswer:
\n\"2nd<\/p>\n

Question 9.
\nFind \\(|\\overrightarrow{\\mathbf{x}}|\\) if for a unit vector \\(\\overrightarrow{\\mathrm{a}},(\\overrightarrow{\\mathrm{x}}-\\overrightarrow{\\mathrm{a}})\\cdot(\\overrightarrow{\\mathrm{x}}+\\overrightarrow{\\mathrm{a}})=12\\)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 10.
\nIf \\(\\overrightarrow{\\mathrm{a}}=2 \\hat{\\mathrm{i}}+2 \\hat{\\mathrm{j}}+3 \\hat{\\mathrm{k}}, \\overrightarrow{\\mathrm{b}}=-\\hat{\\mathrm{i}}+2 \\hat{\\mathrm{j}}+\\hat{\\mathrm{k}}\\) and \\(\\overrightarrow{\\mathrm{c}}=3 \\hat{\\mathrm{i}}+\\hat{\\mathrm{j}}\\) are such that \\(\\overrightarrow{\\mathbf{a}}+\\lambda \\overrightarrow{\\mathbf{b}}\\) is perpendicular to \\(\\overrightarrow{\\mathbf{c}}\\), then the value of \u03bb
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 11.
\nShow that \\(|\\overrightarrow{\\mathbf{a}}| \\overrightarrow{\\mathbf{b}}+|\\overrightarrow{\\mathbf{b}}| \\overrightarrow{\\mathbf{a}}\\) is a perpendicular to \\(|\\overrightarrow{\\mathrm{a}}| \\overrightarrow{\\mathbf{b}}-|\\overrightarrow{\\mathrm{b}}| \\overrightarrow{\\mathrm{a}}\\), for ant two non zero vectors \\(\\overrightarrow{\\mathbf{a}} \\text { and } \\overrightarrow{\\mathbf{b}}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 12.
\nIf \\(\\overrightarrow{\\mathrm{a}} \\cdot \\overrightarrow{\\mathrm{a}}=0 \\text { and } \\overrightarrow{\\mathrm{a}} \\cdot \\overrightarrow{\\mathrm{b}}=0\\), then what can be concluded about the vector \\(\\overrightarrow{\\mathbf{b}}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 13.
\nIf \\(\\overrightarrow{\\mathrm{a}}, \\overrightarrow{\\mathrm{b}}, \\overrightarrow{\\mathrm{c}}\\)are unit vector such that \\(\\overrightarrow{\\mathbf{a}}+\\overrightarrow{\\mathbf{b}}+\\overrightarrow{\\mathbf{c}}=\\overrightarrow{\\mathbf{0}}\\), find the value of \\(\\overrightarrow{\\mathrm{a}} \\cdot \\overrightarrow{\\mathrm{b}}+\\overrightarrow{\\mathrm{b}} \\cdot \\overrightarrow{\\mathrm{c}}+\\overrightarrow{\\mathrm{c}} \\cdot \\overrightarrow{\\mathrm{a}}\\)
\nAnswer:
\n\"2nd
\n\"2nd
\nQuestion 14.
\nIf either vector \\(\\overrightarrow{\\mathbf{a}}=\\overrightarrow{\\mathbf{0}} \\quad \\text { or } \\quad \\overrightarrow{\\mathbf{b}}=\\overrightarrow{\\mathbf{0}}\\) then \\(\\overrightarrow{\\mathbf{a}} \\cdot \\overrightarrow{\\mathbf{b}}=\\overrightarrow{\\mathbf{0}}\\). But the converse need not be true. Justify your answer with an example.
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 15.
\nIf the vertices A, B, C of a triangle ABC are (1, 2, 3), (-1, 0, 0), (0, 1, 2), respectively, then find \u2220ABC, [\u2220ABC is the angle between the vectors \\(\\bar { BA }\\) and \\(\\bar { BC }\\) .
\nAnswer:
\n\"2nd<\/p>\n

Question 16.
\nShow that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, -1) are collinear.
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 17.
\nShow that the vector\\(2 \\hat{i}-\\hat{j}+\\hat{k}, \\hat{i}-3 \\hat{j}-5 \\hat{k}\\) and
\n\\(\\text { and } 3 \\hat{i}-4 \\hat{j}-4 \\hat{k}\\) from the vertices of a right angled triangle:
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 18.
\nIf \\(\\overrightarrow{\\mathbf{a}}\\) is a nonzero vector of magnitude ‘a’ and
\n\u03bb a nonzero scalar then \u03bb \\(\\vec{a}\\) is unit vector if……….
\n(A) \u03bb = 1
\n(B) \u03bb = -1
\n(C) a = |\u03bb|
\n(D) a = 1\/|\u03bb|
\nAnswer:
\n\"2nd<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 10 Vector Algebra Ex 10.3 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 Ex 10.3 2nd PUC Maths Vector Algebra …<\/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\/21141"}],"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=21141"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21141\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=21141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=21141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=21141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}