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JEE Main & Advanced Mathematics Vector Algebra Question Bank Vector or Cross product of two vectors and its application

  • question_answer
    Given \[\mathbf{a}=\mathbf{i}+\mathbf{j}-\mathbf{k},\,\,\mathbf{b}=-\mathbf{i}+2\mathbf{j}+\mathbf{k}\] and \[\mathbf{c}=-\mathbf{i}+2\mathbf{j}-\mathbf{k}.\] A unit vector perpendicular to both \[\mathbf{a}+\mathbf{b}\] and \[\mathbf{b}+\mathbf{c}\] is                                                 [Karnataka CET 1993]

    A)                 i

    B)                 j

    C)                 k

    D)                 \[\frac{\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{3}}\]

    Correct Answer: C

    Solution :

               Obviously, \[\mathbf{b}+\mathbf{c}=-2\mathbf{i}+4\mathbf{j}\] and \[\mathbf{a}+\mathbf{b}=3\mathbf{j}.\]                 Hence the unit vector \[\mathbf{k}\] is perpendicular to both \[\mathbf{b}+\mathbf{c}\] and \[\mathbf{a}+\mathbf{b}.\]


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