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
Answer & explanation
Correct answer: option 1
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
$⇔\vec a.\vec b=\vec b.\vec c=\vec c.\vec a=0$