A) \[3\pi /4\]
B) \[\pi /4\]
C) \[\pi /8\]
D) \[\pi /2\]
Correct Answer: A
Solution :
\[(\hat{a}.\hat{c})\hat{b}-(\hat{a}.\hat{b})\hat{c}=\frac{1}{\sqrt{2}}\hat{b}+\frac{1}{\sqrt{2}}\hat{c}\] \[\therefore \]\[\hat{a}.\hat{c}=\frac{1}{\sqrt{2}}\]and\[\hat{a}.\hat{b}=-\frac{1}{\sqrt{2}}\] \[\Rightarrow \]angle between \[\hat{a}\]and \[\hat{c}=\frac{\pi }{4}\]and angle between \[\hat{a}\]and\[\hat{b}=\frac{3\pi }{4}\]
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