If the vectors `veca, vecb, vecc` and `vecd` are coplanar vectors, then `(vecaxxvecb)xx(veccxxvecd)` is equal to

Options

A. `1`
B. `veca`
C. `vecb`
D. `vec0`

Answer

D

Explanation

Since `veca, vecb, vecc, vecd` are coplanar vectors. Therefore, `vecaxxvecb` and `veccxxvecd` are vectors normal to the plane containing the four vectors.
`:.vecaxxvecb` is parallel `veccxxvecdimplies(vecaxxvecb)xx(veccxxvecd)=vec0`
ALITER We have
`(vecaxxvecb)xx(veccxxvecd)={(vecaxxvecb).vecd}vecc-{(vecaxxvecb).vecc}vecd`
`implies(vecaxxvecb)xx(vecxvecd)=[(veca, vecb, vecd)]vecc-[(veca, vecb, vecc)]veca`
`implies(vecaxxvecb)xx(veccxxvecd)=0xxvecc-0xxvecd [ :'veca, vecb, vecc, vecd` are coplanar `]`
`implies(vecaxxvecb)xx(veccxxvecd)=vec0`