Question

The torque of a force $\overrightarrow{F}=2\hat{i}+\hat{j}+4\hat{k}$ acting at a point $\overrightarrow{r}=7\hat{i}+3\hat{j}+\hat{k}$ is

• 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. $11\hat{i}-26\hat{j}+\hat{k}$

Answer 1

The correct option is D $11\hat{i}-26\hat{j}+\hat{k}$

We know that:

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{f}$

$=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 7& 3& 1\\ 2& 1& 4\end{array}\right|$

$=(12-1)\hat{i}-(28-2)\hat{j}+(7-6)\hat{k}$

$=11\hat{i}-26\hat{j}+\hat{k}$