If `veca, vecb` and `vecc` are unit coplanar vectors, then the scalar triple product `[(2veca-vecb, 2vecb-vecc, 2vecc-veca)]=`

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`