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NEET Sample Paper NEET Sample Test Paper-17

  • question_answer
    The area of the parallelogram determined by\[\vec{A}=2\hat{i}+\hat{j}-2\hat{k}\]and\[\vec{B}=12\hat{j}-2\hat{k}\]is:

    A)  42                 

    B)  56                              

    C)  38                 

    D)  74

    Correct Answer: A

    Solution :

    \[\vec{A}\times \vec{B}=\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    2 & 1 & -3  \\    0 & 12 & -2  \\ \end{matrix} \right|\] \[=\hat{i}(-2+36)-\hat{j}(-4-0)+\hat{k}(24-0)\] \[=34\hat{i}+4\hat{j}+24\hat{k}\] \[|\vec{A}\times \vec{B}|=\sqrt{1156+16+576}\] \[=41.81\approx 42\] Hence, the correction option is [a].


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