question_answer

Directions: Question No. 76 are based on the following paragraph. Let \[\overrightarrow{a},\overrightarrow{b}\]and \[\overrightarrow{c}\]be three vectors such that \[|\overrightarrow{a}|=|\overrightarrow{b}|=|\overrightarrow{c}|=4\]and angel between \[\overrightarrow{a}\]and \[\overrightarrow{b}\]is \[\frac{\pi }{3}\]and angel between \[\overrightarrow{b}\]and \[\overrightarrow{c}\]is \[\frac{\pi }{3}\]and angle between \[\overrightarrow{c}\]and \[\overrightarrow{a}\]is \[\frac{\pi }{3}\] The volume of the tetrahedron whose adjacent edges are represented by the vectors \[\overrightarrow{a},\overrightarrow{b}\] and \[\overrightarrow{c}\]is

A)  \[\frac{16\sqrt{2}}{3}\]                

B)  \[2\sqrt{\frac{2}{3}}\]

C)  \[3\sqrt{\frac{2}{3}}\]                  

D)  \[4\sqrt{\frac{2}{3}}\]