{"id":21205,"date":"2020-01-24T11:06:39","date_gmt":"2020-01-24T05:36:39","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=21205"},"modified":"2021-07-02T15:27:07","modified_gmt":"2021-07-02T09:57:07","slug":"2nd-puc-maths-question-bank-chapter-10-ex-10-4","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-maths-question-bank-chapter-10-ex-10-4\/","title":{"rendered":"2nd PUC Maths Question Bank Chapter 10 Vector Algebra Ex 10.4"},"content":{"rendered":"

Students can Download Maths Chapter 10 Vector Algebra Ex 10.4 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 10.4<\/h2>\n

2nd PUC Maths Vector Algebra NCERT Text Book Questions and Answers Ex 10.4<\/h3>\n

Question 1.
\nFind
\n\\(|\\vec{a} \\times \\vec{b}|, \\text { if } \\vec{a}=\\hat{i}-7 \\hat{j}+7 \\hat{k} \\text { and }\\overrightarrow{\\mathbf{b}}=3 \\hat{\\mathbf{i}}-2 \\hat{\\mathbf{j}}+2 \\hat{\\mathbf{k}}\\)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

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

\"KSEEB<\/p>\n

Question 3.
\nIf a unit vector \\(\\overrightarrow{\\mathrm{a}}\\) makes angles \\(\\frac{\\pi}{3} \\text { with } \\hat{\\mathbf{i}}, \\frac{\\pi}{4}\\) with \\(\\hat{\\mathbf{j}}\\) and acute angle \u03b8 with \\(\\hat{\\mathbf{k}}\\) then find \u03b8 and hence, the component of \\(\\overrightarrow{\\mathrm{a}}\\)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

Question 4.
\nShow that
\n\\((\\overline{\\mathbf{a}}-\\overline{\\mathbf{b}}) \\times(\\overline{\\mathbf{a}}+\\overline{\\mathbf{b}})=\\mathbf{2}(\\overline{\\mathbf{a}} \\times \\overline{\\mathbf{b}})\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 5.
\nFind \u03bb and \u03bc if
\n\\((2 \\hat{\\mathbf{i}}+6 \\hat{\\mathbf{j}}+27 \\hat{\\mathbf{k}}) \\times(\\hat{\\mathbf{i}}+\\lambda \\hat{\\mathbf{j}}+\\mu \\hat{\\mathbf{k}})=\\overrightarrow{\\mathbf{0}}\\)
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 6.
\nGiven that \\(\\overrightarrow{\\mathbf{a}} \\cdot \\overrightarrow{\\mathbf{b}}=\\mathbf{0} \\text { and } \\overrightarrow{\\mathbf{a}} \\times \\overrightarrow{\\mathbf{b}}=\\overrightarrow{\\mathbf{0}}\\). when can you conclude about the vectors \\(\\overrightarrow{\\mathbf{a}} \\text { and } \\overrightarrow{\\mathbf{b}}\\)
\nAnswer:
\n\"2nd
\neither \\(\\bar{a}=0 \\text { or } \\bar{b}=0\\)
\nThey can\u2019t be parallel and perpendicular at the same time.
\n\u2234 At least one of \\(\\bar{a} \\text { and } \\bar{b} \\)is zero \u00a0<\/sup>vector.<\/p>\n

Question 7.
\nLet the vector \\(\\overrightarrow{\\mathrm{a}}, \\overrightarrow{\\mathrm{b}}, \\overrightarrow{\\mathrm{c}}\\) be given as \\(\\mathbf{a}_{1} \\hat{\\mathbf{i}}+\\mathbf{a}_{2} \\hat{\\mathbf{j}}+\\mathbf{a}_{3} \\hat{\\mathbf{k}}, \\mathbf{b}_{1} \\hat{\\mathbf{i}}+\\mathbf{b}_{2} \\hat{\\mathbf{j}}+\\mathbf{b}_{3} \\hat{\\mathbf{k}}, \\mathbf{c} \\hat{\\mathbf{i}}+\\mathbf{c}_{2} \\hat{\\mathbf{j}}+\\mathbf{c}_{3} \\hat{\\mathbf{k}}\\). Then show that \\(\\overrightarrow{\\mathbf{a}} \\times(\\overrightarrow{\\mathbf{b}}+\\overrightarrow{\\mathbf{c}})=\\overrightarrow{\\mathbf{a}} \\times \\overrightarrow{\\mathbf{b}}+\\overrightarrow{\\mathbf{a}} \\times \\overrightarrow{\\mathbf{c}}\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 8.
\nIf either\\(\\overrightarrow{\\mathrm{a}}=\\overrightarrow{0} \\text { or } \\overrightarrow{\\mathrm{b}}=\\overrightarrow{0}, \\text { then } \\overrightarrow{\\mathrm{a}} \\times \\overrightarrow{\\mathrm{b}}=\\overrightarrow{0}\\). Is the converse true? Justify your answer with an example.
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/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).
\nAnswer:
\n\"2nd<\/p>\n

\"2nd<\/p>\n

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

Question 11.
\nLet the vector \\(\\overrightarrow{\\mathbf{a}} \\text { and }\\overrightarrow{\\mathbf{b}}\\) be such that \\(|\\vec{a}|=3 \\text { and }|\\vec{b}|=\\frac{\\sqrt{2}}{3}, \\text { then } \\vec{a} \\times \\vec{b}\\) is a unit vector ,if angle between \\(\\overrightarrow{\\mathbf{a}} \\text { and } \\overrightarrow{\\mathbf{b}} \\text { is }\\)
\n(A) \\(\\pi \/ 6\\)
\n(B) \\(\\pi \/ 4\\)
\n(C) \\(\\pi \/ 3\\)
\n(D) \\(\\pi \/ 2\\)
\nAnswer:
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 12.
\nArea of a rectangle having vertices A, B, C and D with position vectors
\n\\(\\begin{aligned}&-\\hat{\\mathbf{i}}+\\frac{1}{2} \\hat{\\mathbf{j}}+4 \\hat{\\mathbf{k}}, \\hat{\\mathbf{i}}+\\frac{1}{2} \\hat{\\mathbf{j}}+4 \\hat{\\mathbf{k}}, \\hat{\\mathbf{i}}-\\frac{1}{2} \\hat{\\mathbf{j}}+4 \\hat{\\mathbf{k}} \\text { and }\\\\&-\\hat{\\mathbf{i}}-\\frac{1}{2} \\hat{\\mathbf{j}}+4 \\hat{\\mathbf{k}}, \\text { respectively is }\\end{aligned}\\)
\n(A) \\(\\frac{1}{2}\\)
\n(B) 1
\n(C) 2
\n(D) 3
\nAnswer:
\n\"2nd<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 10 Vector Algebra Ex 10.4 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 10.4 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\/21205"}],"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=21205"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/21205\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=21205"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=21205"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=21205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}