A) \[\frac{2\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{2}\]
E) \[\frac{\pi }{6}\]
Correct Answer: D
Solution :
Given that \[(\overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c}=-\frac{1}{4}|\overrightarrow{b}||\overrightarrow{c}|\overrightarrow{a}\] \[\Rightarrow \] \[(\overrightarrow{c}.\overrightarrow{a})\overrightarrow{b}-(\overrightarrow{c}.\overrightarrow{b})\overrightarrow{a}=-\frac{1}{4}|\overrightarrow{b}||\overrightarrow{c}|\overrightarrow{a}\] \[\Rightarrow \] \[(\overrightarrow{c}.\overrightarrow{a})\overrightarrow{b}=0\] \[\Rightarrow \] \[|\overrightarrow{c}||\overrightarrow{a}|\cos \theta =0\Rightarrow \theta =\frac{\pi }{2}\]You need to login to perform this action.
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