The moment of the force $\mathrm{F} = 4\hat{\mathrm{i}} + 5\hat{\mathrm{j}} - 6\hat{\mathrm{k}}$ at (2, 0, -3) about the point (2, -2, -2) is given by:

$\begin{array}{l}\mathrm{We} \mathrm{have}, \overrightarrow{\mathrm{\tau }}=\left(\overrightarrow{\mathrm{r}}-\overrightarrow{{\mathrm{r}}_{\mathrm{o}}}\right)\times \overrightarrow{\mathrm{F}} ; \overrightarrow{{\mathrm{r}}_0}=2\mathrm{i}-2\mathrm{j}-2\mathrm{k} ; \overrightarrow{\mathrm{r}}=2\mathrm{i}+0\mathrm{j}-3\mathrm{k}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\\ \mathrm{Hence}, \overrightarrow{\mathrm{r}}-\overrightarrow{{\mathrm{r}}_{\mathrm{o}}}=(2\mathrm{i}-0\mathrm{j}-3\mathrm{k})-(2\mathrm{i}-2\mathrm{j}-2\mathrm{k})=0\mathrm{i}+2\mathrm{j}-\mathrm{k}\end{array}$

$$\begin{gathered} \overrightarrow{\mathrm{\tau }}=\left|\begin{array}{ccc}\mathrm{i}& \mathrm{j}& \mathrm{k}\\ 0& 2& -1\\ 4& 5& -6\end{array}\right| \\ \overrightarrow{\mathrm{\tau }}=-7\hat{\mathrm{i}}-4\hat{\mathrm{j}}-8\hat{\mathrm{k}} \end{gathered}$$