BCECE Medical BCECE Medical Solved Papers-2009

  • question_answer What is the torque of force \[\vec{F}=3\,\hat{i}+\hat{j}+5\hat{k}\]acting at point whose position vector is\[\vec{r}=7\,\hat{i}+3\hat{j}+\hat{k}\]?

    A)  \[14\,\hat{i}-38\hat{j}+16\,\hat{k}\]

    B)  \[4\,\hat{i}+4\hat{j}+6\,\hat{k}\]

    C)  \[14\,\hat{i}+38\hat{j}-16\,\hat{k}\]

    D)  \[-21\,\hat{i}+3\hat{j}+5\,\hat{k}\]

    Correct Answer: C

    Solution :

    Torque \[\tau =\vec{F}\times \vec{r}\]                 \[=(-3\hat{i}+\hat{j}+5\hat{k})\times (7\hat{i}+3\hat{j}+\hat{k})\] or            \[\vec{\tau }=\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    -3 & 1 & 5  \\    7 & 3 & 1  \\ \end{matrix} \right|\] \[=-14\hat{i}+38\hat{j}-16\hat{k}\]

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