Answer
$$M_{B C}=165 \mathrm{~N} \cdot \mathrm{m}
$$
Work Step by Step
$$
\begin{aligned}
& \mathbf{u}_{B C}=\frac{\mid-1.5 \mathbf{i}-2.5 \mathbf{j}\}}{\sqrt{(-1.5)^2+(-2.5)^2}} \\
& \mathbf{u}_{B C}=\{-0.5145 \mathbf{i}-0.8575 \mathbf{j}\} \\
& M_{B C}=\mathbf{u}_{B C} \cdot\left(\mathbf{r}_{C D} \times \mathbf{F}\right)=\left|\begin{array}{ccc}
-0.5145 & -0.8575 & 0 \\
0.5 & 2 & 4 \\
50 & -20 & -80
\end{array}\right| \\
& M_{B C}=165 \mathrm{~N} \cdot \mathrm{m}
\end{aligned}
$$
