question_answer

If \[\vec{a}\] is perpendicular to\[\overrightarrow{b}\]and\[\overrightarrow{c},|\overrightarrow{a}|=2,\]\[|\overrightarrow{b}|=3|\overrightarrow{c}|=4\]and the angle between\[\overrightarrow{b}\]and\[\overrightarrow{c}\]is\[\frac{2\pi }{3},\]then\[[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}]\]is equal to:

A)  \[4\sqrt{3}\]                                     

B)  \[6\sqrt{3}\]

C)  \[12\sqrt{3}\]                  

D)         \[18\sqrt{3}\]

E)  \[8\sqrt{3}\]