Question

Find the torque of a force $7\hat{i}+3\hat{j}-5\hat{k}$ about the origin. The force acts on a particle whose position vector is $\hat{i}-\hat{j}+\hat{k}$.

Answer 1

Here $r=\hat{i}-\hat{j}+\hat{k}$
and $F=7\hat{i}+3\hat{j}-5k$.
We shall use the determinant rule to find the torque $\tau =r\times F$
$\tau =\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -1& 1\\ 7& 3& -5\end{array}\right|$ $=(5-3)\hat{i}-(-5-7)\hat{j}+(3-(-7\left)\right)\hat{k}$
or $\tau =2\hat{i}+12\hat{j}+10\hat{k}$