Let a force \(\overrightarrow{\mathrm{F}}=-\mathrm{F} \mathrm{k}\) acts on the origin of cartesian frame of reference. The moment of force about a point \((1,-1)\) will be

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 \(\mathrm{P}\):
\(\Rightarrow \vec{\tau}=\overrightarrow{\mathrm{PO}} \times \overrightarrow{\mathrm{F}}=(-\hat{\mathrm{i}}+\hat{\mathrm{j}}) \times(-\mathrm{F} \hat{\mathrm{k}})\)
\(\Longrightarrow \vec{\tau}=\mathrm{F}[(\hat{\mathrm{i}} \times \hat{\mathrm{k}})+\hat{\mathrm{k}} \times \hat{\mathrm{j}}]\)
Using: \(\hat{\mathrm{i}} \times \hat{\mathrm{j}}=\hat{\mathrm{k}} ; \hat{\mathrm{j}} \times \hat{\mathrm{k}}=\hat{\mathrm{i}} ; \hat{\mathrm{k}} \times \hat{\mathrm{i}}=\hat{\mathrm{j}}\)
\(\Rightarrow \vec{\tau}=\mathrm{F}(-\hat{\mathrm{i}}-\hat{\mathrm{j}})=-\mathrm{F}(\hat{\mathrm{i}}+\hat{\mathrm{j}})\)