Non-zero vector related question

Question

For non−zero vectors $\bar a ,\bar b ,\bar c $ , $|\bar a ×\bar b .\bar c |=|\bar a||\bar b||\bar c|$, holds if only if

(A) $\bar a\cdot\bar b=0 , \bar b\cdot\bar c=0 $

(B) $\bar c\cdot\bar a=0 , \bar a\cdot\bar b=0 $

(C) $\bar a\cdot\bar c=0 , \bar b\cdot\bar c=0 $

(D) $\bar c\cdot\bar a =\bar a\cdot\bar b=\bar b\cdot\bar c=0 $

My approach is as follow $\bar t=\bar a ×\bar b$

$\bar t\cdot\bar c =|\bar t||\bar c|\cos\theta$

$\bar t=\bar a ×\bar b$

$\frac{\bar a ×\bar b}{|\bar a| |\bar b|}=\sin\theta$

$\bar a ×\bar b=|\bar a| |\bar b|\sin\theta$

After this step I am not able to proceed

Answer 1

Hint.
$|\bar a ×\bar b .\bar c |$ is the volume of the parallelepiped whose adjacent sides are the vectors $a$, $b$, and $c$.