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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 \[|\mathbf{a}|\,=4,\,|\mathbf{b}|\,=2\]  and the angle between a and b  is \[\frac{\pi }{6}\], then \[{{(\mathbf{a}\times \mathbf{b})}^{2}}\] is equal to [AIEEE 2002]       

    A)                 48

    B)                 16

    C)                 8

    D)                 None of these

    Correct Answer: B

    Solution :

               \[{{(\mathbf{a}\times \mathbf{b})}^{2}}={{(|\mathbf{a}||\mathbf{b}|\,\,\sin \theta )}^{2}}\]                                                 \[={{(4.2\,\,\sin \,{{30}^{o}})}^{2}}={{\left( 8.\frac{1}{2} \right)}^{2}}={{4}^{2}}\]\[=16\].


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