দুটি ভেক্টর    $\overline{P} = 2 \hat{i} - 3 \hat{j} - \overline{k}$ এবং   $\overline{Q} = \hat{i} + 4 \hat{j} - 2 \overline{k}$   দ্বারা গঠিত সমতলের উপর একক লম্ব ভেক্টর কত ?  

$\overrightarrow{\mathrm{P}} \times \overrightarrow{\mathrm{Q}}=\left|\begin{array}{ccc}\hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 2 & -3 & -1 \\ 1 & 4 & -2\end{array}\right|=\hat{\mathrm{i}}(6+4)+\hat{\mathrm{j}}(-1+4)+\hat{\mathrm{k}}(8+3)=10 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+11 \hat{\mathrm{k}}$

$|\overrightarrow{\mathrm{P}} \times \overrightarrow{\mathrm{Q}}|=\sqrt{10^{2}+3^{2}+11^{2}}=\sqrt{230} \therefore$ নির্ণেরয় একক ভেক্টর $= \pm \frac{\overrightarrow{\mathrm{P}} \times \overrightarrow{\mathrm{Q}}}{|\overrightarrow{\mathrm{P}} \times \overrightarrow{\mathrm{Q}}|}= \pm \frac{1}{\sqrt{230}}(10 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+11 \hat{\mathrm{k}})$