IIT-JEE 2000 ScreeningQuestion 1
If $\vec a,\vec b$ and $\vec c$ are unit coplanar vectors, then the scalar triple product $\left[2\vec a-\vec b,\ 2\vec b-\vec c,\ 2\vec c-\vec a\right]=$
Vector Algebra
Solution
$[2\vec a-\vec b,\,2\vec b-\vec c,\,2\vec c-\vec a]=7[\vec a\,\vec b\,\vec c]$, and coplanar vectors have $[\vec a\,\vec b\,\vec c]=0$, so the value is $0$.