If $\vec a,\vec b,\vec c, \vec d$ are coplanar vectors, then $(\vec a×\vec b)×(\vec c×\vec d)=$
Answer & explanation
Correct answer: option 4
Since $\vec a,\vec b,\vec c, \vec d$ are coplanar vectors. Therefore, $\vec a×\vec b$ and $\vec c×\vec d$ are vectors normal to the plane containing the four vectors.
$∴\vec a×\vec b$ is parallel to $\vec c×\vec d$ $⇒(\vec a×\vec b)×(\vec c×\vec d)=\vec 0$