A) \[\pm \,\frac{1}{\sqrt{6}}\,(2\mathbf{i}+\mathbf{j}+\mathbf{k})\]
B) \[\frac{1}{\sqrt{6}}\,(\mathbf{i}+2\mathbf{j}+\mathbf{k})\]
C) \[\frac{1}{\sqrt{6}}\,(\mathbf{i}+\mathbf{j}+\mathbf{k})\]
D) \[\frac{1}{\sqrt{6}}\,(2\mathbf{i}-\mathbf{j}-\mathbf{k})\]
Correct Answer: A
Solution :
\[\mathbf{a}=\mathbf{i}+\mathbf{j}-3\mathbf{k},\] \[\mathbf{b}=-2\mathbf{i}+2\mathbf{j}+2\mathbf{k}\] \[\mathbf{a}\times \mathbf{b}=\left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 1 & -3 \\ -2 & 2 & 2 \\ \end{matrix} \right|=8\mathbf{i}+4\mathbf{j}+4\mathbf{k}\] Hence unit vector \[=\pm \frac{2\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{6}}.\]
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