Question

A force $\overrightarrow{F}=(2\hat{i}+3\hat{j}+4\hat{k})N$ is applied to a point having position vector $\overrightarrow{r}=(3\hat{i}+2\hat{j}+\hat{k})m$.
Find the torque due to the force about the axis passing through origin.

Answer 1

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}=(3\hat{i}+2\hat{j}+\hat{k})\times (2\hat{i}+3\hat{j}+4\hat{k})=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& 2& 1\\ 2& 3& 4\end{array}\right|$;

$\overrightarrow{\tau }=(5\hat{i}+10\hat{j}+5\hat{k})N-m$

$\tau =\sqrt{(5{)}^2-(-10{)}^2+(5{)}^2}N-m$
$\Rightarrow \tau =5\surd 6N-m$.