Physics - Rotation Question with Solution | TestHub

Position vector $\vec{r}=\mathrm{PO}=\overrightarrow{\mathrm{O}}-(1\hat{i}-1\hat{\mathrm{j}})=-\hat{i}+\hat{j}$ Torque about point $P,\vec{\tau }=\vec{r}\times \vec{F}$ $\begin{array}{rl}& \therefore \vec{\tau }=(-\hat{i}+\hat{j})\times (-F\hat{k})\\ & \text{OR }\vec{\tau }=F[(\hat{i}\times \hat{k})-(\hat{j}\times \hat{k})]=F[-\hat{j}-\hat{i}]\\ & \Rightarrow \vec{\tau }=-F[\hat{i}+\hat{j}]\end{array}$