Question

A force $\overrightarrow{ F }=(\hat{ i }+2 \hat{ j }+3 \hat{ k }) N$ acts at a point $(4 \hat{ i }+3 \hat{ j }-\hat{ k }) m \cdot$ Then the magnitude of torque about the point $(\hat{ i }+2 \hat{ j }+\hat{ k }) m$ will be $\sqrt{ x } N - m .$ The value of $x$ is ____.

Answer 1

$\vec{\tau}=\left(\vec{ r }_{2}-\vec{ r }_{1}\right) \times \vec{ F }$
$=[(4 \hat{ i }+3 \hat{ j }-\hat{ k })-(\hat{ i }+2 \hat{ j }+\hat{ k })] \times \vec{ F }$
$=(3 \hat{ i }+\hat{ j }-2 \hat{ k }) \times(\hat{ i }+2 \hat{ j }+3 \hat{ k })$
$\tau=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\ 3&1&-2\\ 1&2&3\end{vmatrix}$
$=7 \hat{i}-11 \hat{j}+5 \hat{k}$
$|\vec{\tau}|=\sqrt{195}$