• # 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)  $-21\,\hat{i}+3\hat{j}+5\,\hat{k}$

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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