Sol. $$ \begin{aligned} & \overrightarrow{\mathrm{P}} \times \overrightarrow{\mathrm{Q}}=\left|\begin{array}{ccc} \hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 3 & \sqrt{3} & 2 \\ 4 & \sqrt{3} & 2.5 \end{array}\right|=\sqrt{3} \frac{\hat{\mathrm{i}}}{2}+\frac{\hat{\mathrm{j}}}{2}-\sqrt{3 \hat{\mathrm{k}}} \\ & \Rightarrow \frac{\overrightarrow{\mathrm{P}} \times \overrightarrow{\mathrm{Q}}}{|\overrightarrow{\mathrm{P}} \times \overrightarrow{\mathrm{Q}}|}=\frac{1}{2}\left(\sqrt{3} \frac{\hat{\mathrm{i}}}{2}+\frac{\hat{\mathrm{j}}}{2}-\sqrt{3 \hat{\mathrm{k}}}\right)=\frac{1}{4}(\sqrt{3} \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \sqrt{3} \hat{\mathrm{k}}) \quad x=4 \end{aligned} $$