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

  • question_answer
    The moment of a force represented by \[\overrightarrow{F}=\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] about the point \[2\,\mathbf{i}-\mathbf{j}+\mathbf{k}=\]                                  [BIT Ranchi 1992]

    A)                 \[5\mathbf{i}-5\mathbf{j}+5\mathbf{k}\]

    B)                 \[5\mathbf{i}+5\mathbf{j}-5\mathbf{k}\]

    C)                 \[-5\mathbf{i}+5\mathbf{j}+5\mathbf{k}\]

    D)                 \[-5\mathbf{i}-5\mathbf{j}+5\mathbf{k}\]

    Correct Answer: D

    Solution :

                    \[\mathbf{r}\times \mathbf{F}=\left| \begin{matrix}    \mathbf{i} & \mathbf{j} & \mathbf{k}  \\    2 & -1 & 1  \\    1 & 2 & 3  \\ \end{matrix} \right|=-5\mathbf{i}-5\mathbf{j}+5\mathbf{k}.\]


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