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

  • question_answer
    If \[{{(\mathbf{a}\times \mathbf{b})}^{2}}+{{(\mathbf{a}\,\,.\,\,\mathbf{b})}^{2}}=144\] and \[|\mathbf{a}|\,=4,\] then \[|\mathbf{b}|\,=\]                                                 [EAMCET 1994]

    A)                 16

    B)                 8

    C)                 3

    D)                 12

    Correct Answer: C

    Solution :

               We know that \[{{(\mathbf{a}\times \mathbf{b})}^{2}}+{{(\mathbf{a}\,.\,\mathbf{b})}^{2}}=\,|\mathbf{a}{{|}^{2}}|\mathbf{b}{{|}^{2}}\]                 \[\therefore \,\,\,144=16|\mathbf{b}{{|}^{2}}\Rightarrow \,|\mathbf{b}|=3.\]


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