Answer
$$
\mathbf{M}_B=\{-110 \mathbf{i}-180 \mathbf{j}-420 \mathbf{k}\} \mathrm{N} \cdot \mathrm{m}
$$
Work Step by Step
The coordinates of points $B$ and $C$ are $B(0.5,0,0) \mathrm{m}$ and $C(0.5,0.7,-0.3) \mathrm{m}$, respectively.
$$
\begin{aligned}
\mathbf{r}_{B C} & =(0.5-0.5) \mathbf{i}+(0.7-0) \mathbf{j}+(-0.3-0) \mathbf{k} \\
& =\{0.7 \mathbf{j}-0.3 \mathbf{k}\} \mathrm{m}
\end{aligned}
$$
Moment of Force $\boldsymbol{F}$ About Point $\boldsymbol{B}$.
$$
\begin{aligned}
\mathbf{M}_B & =\mathbf{r}_{B C} \times \mathbf{F} \\
& =\left|\begin{array}{ccc}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
0 & 0.7 & -0.3 \\
600 & 800 & -500
\end{array}\right| \\
& =\{-110 \mathbf{i}-180 \mathbf{j}-420 \mathbf{k}\} \mathrm{N} \cdot \mathrm{m}
\end{aligned}
$$
