question_answer

Let a, b and c be non-zero vectors such that\[(\overrightarrow{a}.\overrightarrow{b})\times \overrightarrow{c}=\frac{-1}{4}|\overrightarrow{b}||\overrightarrow{c}|\overrightarrow{a}.\]. If\[\theta \]is the acute angle between the vectors \[\vec{b}\] and \[\vec{c}\], then the angle between\[\overrightarrow{a}\]and\[\overrightarrow{c}\]is equal to

A)  \[\frac{2\pi }{3}\]                                           

B)  \[\frac{\pi }{4}\]

C)  \[\frac{\pi }{3}\]                             

D)         \[\frac{\pi }{2}\]

E)  \[\frac{\pi }{6}\]