Question

Find the torque of a force $\overrightarrow{F}=-3\hat{i}+\hat{j}+5\hat{k}$ acting at the point $\overrightarrow{r}=7\hat{i}+3\hat{j}+\hat{k}$ with respect to origin:-

• A. $14\hat{i}-32\hat{j}-2\hat{k}$
• B. $4\hat{i}+4\hat{j}+6\hat{k}$
• C. $-14\hat{i}+38\hat{j}-16\hat{k}$
• D. $-21\hat{i}+3\hat{j}+5\hat{k}$

Answer 1

The correct option is A $14\hat{i}-32\hat{j}-2\hat{k}$

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}=(7\hat{i}+3\hat{j}+\hat{k})(-3\hat{i}+\hat{j}+5\hat{k})$

$\overrightarrow{\tau }=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 7& 3& 1\\ -3& 1& 5\end{array}\right|=14\hat{i}-38\hat{j}+16\hat{k}$