If `veca, vecb, vecc` are non-coplanar non-zero vectors, then
`(vecaxxvecb)xx(vecaxxvecc)+(vecbxxvecc)xx(vecbxxveca)+veccxxveca)xx(vecxxvecb)` is equal to

Options

A. `[(veca, vecb, vecc)]^(2)(veca+vecb+vecc)`
B. `[(veca, vecb, vecc)](veca+vecb+vecc)`
C. `vec0`
D. none of these

Answer

B

Explanation

We have
`(vecaxxvecb)xx(vecaxxvecc)={(vecaxxvecb).vecc}veca-{(vecaxxvecb).veca}vecc`
`implies (vecaxxvecb)xx(vecaxxvecc)=[(veca, vecb, vecc)]veca-[(veca, vecb, veca)]vecc=[(veca, vecb, vecc)]=[(veca, vecb, vecc)]veca`
Similarly we have
`(vecbxxvecc)(vecbxxveca)=[(vecb, vecc, veca)]vecb` and `(veccxxveca)xx(veccxxvecb)=[(vecc, veca, vecb)]vecc`
So the given expression is equal to `[(veca, vecb,vecc)](veca+vecb+vecc)`