A) \[\frac{3\pi }{4}\]
B) \[\frac{\pi }{4}\]
C) \[\pi /2\]
D) \[\pi \]
Correct Answer: A
Solution :
Since \[\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})=\frac{\overrightarrow{b}+\overrightarrow{c}}{\sqrt{2}}\] \[\Rightarrow \,\,(\overrightarrow{a}.\overrightarrow{c})\overrightarrow{b}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c}=\frac{1}{\sqrt{2}}\overrightarrow{b}+\frac{1}{\sqrt{2}}\overrightarrow{c}\] \[\Rightarrow \,\,\overrightarrow{a}.\overrightarrow{c}\,\,=\frac{1}{\sqrt{2}}\] [\[\because \,\,\overrightarrow{b}\] and \[\overrightarrow{c}\] are non coplanar]\ and \[\overrightarrow{a}.\overrightarrow{b}=-\frac{1}{\sqrt{2}}\Rightarrow \cos \theta =-\frac{1}{\sqrt{2}}\] [\[\because \,\overrightarrow{a},\overrightarrow{b}\] are unit vectors] \[\Rightarrow \,\,\cos \frac{3\pi }{4}=\cos \theta \Rightarrow \theta =3\pi /4\]
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