For non-coplanar vectors $\vec a,\vec b$ and $\vec c$, the relation $|(\vec a×\vec b). \vec c|=|\vec a||\vec b||\vec c|$ holds iff

$\vec a.\vec b=\vec b.\vec c=\vec c.\vec a=0$

We have,

$|(\vec a×\vec b). \vec c|=|\vec a||\vec b||\vec c|$

⇔ Volume of the parallelopiped having $\vec a,\vec b$ and $\vec c$ as three coterminus edges is equal to $|\vec a||\vec b||\vec c|$

$⇔\vec a,\vec b,\vec c$ are along mutually perpendicular edges

$⇔\vec a.\vec b=\vec b.\vec c=\vec c.\vec a=0$