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