$a = 3 \hat{i} + 2 \hat{j} + 2 \hat{k}$ এবং $b = \hat{i} + 2 \hat{j} - 2 \hat{k}$  হলে a+b ও a-b ভেক্টরদ্বয়ের লম্ব বরাবর একক ভেক্টর নিচের কোনটি?

$\mathbf{a}+\mathbf{b}=4 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}$

$\begin{array}{l} \mathbf{a}-\mathbf{b}=2 \hat{\mathrm{i}}+4 \hat{\mathrm{k}} \\ \begin{array}{r} \therefore(\mathbf{a}+\mathbf{b}) \times(\mathbf{a}-\mathbf{b})=\left|\begin{array}{ccc} \hat{\mathrm{i}} & \hat{\mathrm{j}} \cdot \hat{\mathrm{k}} \\ 4 & 4 & 0 \\ 2 & 0 & 4 \end{array}\right| \\ =16 \hat{\mathrm{i}}-16 \hat{\mathrm{j}}-8 \hat{\mathrm{k}} \end{array} \\ \text { বा, }|(\mathbf{a}+\mathbf{b}) \times(\mathbf{a}-\mathbf{b})|=\sqrt{576}=24 . \\ \therefore \text { একक ভেক্টর }= \pm \frac{16 \hat{\mathrm{i}}-16 \hat{\mathrm{j}}-8 \hat{\mathrm{k}}}{24} \\ \therefore \quad \therefore= \pm \frac{1}{3}(2 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}-\hat{\mathrm{k}}) \end{array}$