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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 \[3\mathbf{i}+4\mathbf{j}\] and \[-5\mathbf{i}+7\mathbf{j}\] are the vector sides of any triangle, then its area is given by [RPET 1987, 90]

    A)                 41

    B)                 47

    C)                 \[\frac{41}{2}\]

    D)                 \[\frac{47}{2}\]

    Correct Answer: C

    Solution :

               Area is given by,                                 \[\frac{1}{2}|(3\mathbf{i}+4\mathbf{j})\times (-5\mathbf{i}+7\mathbf{j})|\]\[=\frac{1}{2}|(41)\mathbf{k}|\,=\,\,\frac{41}{2}\].


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