A) i
B) j
C) k
D) None of these
Correct Answer: D
Solution :
\[\mathbf{c}=\lambda \mathbf{a}+\mu \mathbf{b}=(\lambda +\mu )\mathbf{i}-\lambda \mathbf{j}+\mu \mathbf{k}\] Now, \[\mathbf{c}.\mathbf{a}=0\Rightarrow 2\lambda +\mu =0\Rightarrow \mu =-2\lambda \] Therefore, \[\mathbf{c}=-\lambda \mathbf{i}-\lambda \mathbf{j}-2\lambda \mathbf{k}=(\sqrt{6})(-\lambda )\left[ \frac{\mathbf{i}+\mathbf{j}+2\mathbf{k}}{\sqrt{6}} \right]\] Hence, unit vector \[=\frac{(\mathbf{i}+\mathbf{j}+2\mathbf{k})}{\sqrt{6}}\].
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