If `veca,vecb, vecc` are unit coplanar vectors then the scalar triple product `[2veca-vecb, 2vecb-c ,vec2c-veca]` is equal to (A) `0` (B) `1` (C) `-sqrt(3)` (D) `sqrt(3)`

Options

A. `0`
B. `1`
C. `-sqrt(3)`
D. `sqrt(3)`

Answer

A

Explanation

Since `veca, vecb, vecc` are coplanar vectors.
`:.[(veca, vecb, vecc)]=0`
Let `vec(alpha)=2veca-vecb, vec(beta)=2vecb-vecc` and `vec(gamma)=2vecc-veca` Then
`[(vec(alpha),vec(beta),vec(gamma))]=|(2,-1,0),(0,2,-1),(-1,0,2)|=[(veca, vecb, vecc)]`
`implies[(vec(alpha), vec(beta), vec(gamma))]=7[(veca, vecb, vecc)]=7xx0=0`