Physics - Rotation Question with Solution | TestHub

Torque in vector form is expressed as vector multiplication of position vector and force.

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

$\Rightarrow \overrightarrow{\tau }=\left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ 2& 1& 2\\ 3& 4& -2\end{array}\right|$

$\Rightarrow \overrightarrow{\tau }=\left(-2-8\right)\hat{\mathrm{i}}-\left(-4-6\right)\hat{\mathrm{j}}+\left(8-3\right)\hat{\mathrm{k}}$

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