Answer
$$
F=832 \mathrm{~N}
$$
Work Step by Step
$$
\begin{aligned}
\mathbf{M}_C & =\mathbf{r}_{A B} \times(F \mathbf{k}) \\
& =(0.2 \mathbf{i}+0.3 \mathbf{j}) \times(F \mathbf{k}) \\
& =\{0.2 F \mathbf{i}-0.3 F \mathbf{j}\} \mathrm{N} \cdot \mathrm{m} \\
M_C & =F \sqrt{(0.2 F)^2+(-0.3 F)}=0.3606 F \\
300 & =0.3606 F \\
F & =832 \mathrm{~N}
\end{aligned}
$$
