A) \[{{\cos }^{-1}}\left( \frac{1}{\sqrt{15}} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{4}{\sqrt{15}} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{4}{15} \right)\]
D) \[\frac{\pi }{2}\]
Correct Answer: D
Solution :
\[(\mathbf{i}-\mathbf{j}+\mathbf{k})\,.\,(\mathbf{i}+2\mathbf{j}+\mathbf{k})=\sqrt{3}\sqrt{6}\cos \theta \] \[\Rightarrow \cos \theta =\frac{0}{\sqrt{3}\sqrt{6}}\Rightarrow \theta =\frac{\pi }{2}.\]
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