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JEE Main & Advanced Mathematics Vector Algebra Question Bank Self Evaluation Test - Vector Algebra

  • question_answer
    Force \[\hat{i}+2\hat{j}-3\hat{k},2\hat{i}+3\hat{j}+4\hat{k}\] and \[-\hat{i}-\hat{j}+\hat{k}\] are acting at the point P (0, 1, 2). The moment of these forces about the point A (1, - 2, 0) is

    A) \[2\hat{i}-6\hat{j}+10\hat{k}\]

    B) \[-2\hat{i}+6\hat{j}-10\hat{k}\]

    C) \[2\hat{i}+6\hat{j}-10\hat{k}\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] If \[\vec{F}\] be the resultant force, then \[\vec{F}=2\hat{i}+4\hat{j}+2\hat{k}\] Also, \[\vec{r}=\overrightarrow{AP}=-\hat{i}+3\hat{j}+2\hat{k}\] \[\therefore \] required moment \[=\vec{r}\times \vec{F}=\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    -1 & 3 & 2  \\    2 & 4 & 2  \\ \end{matrix} \right|=-2\hat{i}+6\hat{j}-10\hat{k}\]


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