Physics - Rotation Question with Solution | TestHub

The point $\mathrm{P}$ lies at $(1,-1)$ i.e, $\overrightarrow{\mathrm{P}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}$ $\Rightarrow \overrightarrow{\mathrm{PO}}=\overrightarrow{\mathrm{O}}-\overrightarrow{\mathrm{P}}=-\hat{\mathrm{P}}=-\hat{\mathrm{i}}+\hat{\mathrm{j}}$ Torque about point $\mathrm{P}$: $\Rightarrow \vec{\tau }=\overrightarrow{\mathrm{PO}}\times \overrightarrow{\mathrm{F}}=(-\hat{\mathrm{i}}+\hat{\mathrm{j}})\times (-\mathrm{F}\hat{\mathrm{k}})$ $⟹\vec{\tau }=\mathrm{F}[(\hat{\mathrm{i}}\times \hat{\mathrm{k}})+\hat{\mathrm{k}}\times \hat{\mathrm{j}}]$ Using: $\hat{\mathrm{i}}\times \hat{\mathrm{j}}=\hat{\mathrm{k}};\hat{\mathrm{j}}\times \hat{\mathrm{k}}=\hat{\mathrm{i}};\hat{\mathrm{k}}\times \hat{\mathrm{i}}=\hat{\mathrm{j}}$ $\Rightarrow \vec{\tau }=\mathrm{F}(-\hat{\mathrm{i}}-\hat{\mathrm{j}})=-\mathrm{F}(\hat{\mathrm{i}}+\hat{\mathrm{j}})$