Question

A force of $(2\hat{i}-4\hat{j}+2\hat{k})$N acts at a point $(3\hat{i}+2\hat{j}-4\hat{k})$ metre from the origin. The magnitude of torque is

• A. Zero
• B. 24.4 N-m
• C. 0.244 N-m
• D. 2.444 N-m

Answer 1

The correct option is B 24.4 N-m

$\overrightarrow{F}=(2\hat{i}-4\hat{j}+2\hat{k})N$ and $\overrightarrow{r}=(3i+2-4\hat{k})$ meter
Torque $\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 2& -4\\ 2& -4& 2\end{array}\right|\Rightarrow \overrightarrow{\tau }=-12\hat{i}-14\hat{j}-16\hat{j}-16\hat{k}and|\overrightarrow{\tau }|=\sqrt{(-12{)}^2+(-14{)}^2+(-16{)}^2}=$
24.4 N-m