Question

$$\begin{gathered} \overrightarrow{F}=4\hat{i}+5\hat{j}-6\hat{k} \\ \overrightarrow{r}=(2-2)\hat{i}+(0-(-2\left)\right)\hat{j}+(-3-(-2\left)\right)\hat{k}=2\hat{j}-1\hat{k} \\ \overrightarrow{r}\times \overrightarrow{F}=\left(2\hat{j}-1\hat{k}\right)\times 4\hat{i}+5\hat{j}-6\hat{k} \\ =\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 0& 2& -1\\ 4& 5& -6\end{array}\right|=-7\hat{i}-4\hat{j}-8\hat{k} \end{gathered}$$