Question

A force $7\hat{i}+3\hat{j}-\hat{k}$ acts on a particle whose position vector is $\hat{i}-\hat{j}+\hat{k}$. The torque of the given force about the origin is

• A. $-2\hat{i}+8\hat{j}+10\hat{k}$
• B. $2\hat{i}+8\hat{j}+10\hat{k}$
• C. $2\hat{i}-8\hat{j}+10\hat{k}$
• D. $2\hat{i}+8\hat{j}-10\hat{k}$

Answer 1

The correct option is A $-2\hat{i}+8\hat{j}+10\hat{k}$

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -1& 1\\ 7& 3& -1\end{array}\right|$
$\overrightarrow{\tau }=\hat{i}(1-3)-\hat{j}(-1-7)+\hat{k}(3+7)$
$=-2\hat{i}+8\hat{j}+10\hat{k}$