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

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    The unit vector perpendicular to the vectors \[6\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] and \[3\mathbf{i}-6\mathbf{j}-2\mathbf{k},\] is                                                 [IIT 1989; RPET 1996]

    A)                 \[\frac{2\mathbf{i}-3\mathbf{j}+6\mathbf{k}}{7}\]      

    B)                 \[\frac{2\mathbf{i}-3\mathbf{j}-6\mathbf{k}}{7}\]

    C)                 \[\frac{2\mathbf{i}+3\mathbf{j}-6\mathbf{k}}{7}\]

    D)                 \[\frac{2\mathbf{i}+3\mathbf{j}+6\mathbf{k}}{7}\]

    Correct Answer: C

    Solution :

                    Unit vector perpendicular to both the given vectors is, \[\frac{(6\mathbf{i}+2\mathbf{j}+3\mathbf{k})\times (3\mathbf{i}-6\mathbf{j}-2\mathbf{k})}{|(6\mathbf{i}+2\mathbf{j}+3\mathbf{k})\times (3\mathbf{i}-6\mathbf{j}-2\mathbf{k})|}=\frac{2\mathbf{i}+3\mathbf{j}-6\mathbf{k}}{7}\].


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