Question

If `veca, vecb, vecc` are three non coplanar, non zero vectors then `(veca.veca)(vecbxxvecc)+(veca.vecb)(veccxxveca)+(veca.vecc)(vecaxxvecb)` is equal to
A. `[(veca, vecb, vecc)]vecc`
B. `[(vecb, vecc, veca)]veca`
C. `[(vecc, veca, vecb)]vecb`
D. none of these

Answer 1

Correct Answer - B
Since `veca, vecb, vecc` are three non-coplanar vectors.
Therefore so are for the vectors `vecaxxvecb, vecbxxvecc, veccxxveca`
We know that any vector is space is expressible as the linear combination of three non-coplanar vectors. So let
`veca=x(vecbxxvecc)+y(veccxxveca)+z(vecaxxvecb)`...........i
Taking dot products successively with `veca, vecb, vecc` we get
`x=(veca.veca)/([(veca, vecb, vecc)]),y=(veca.vecb)/([(veca, vecb, vecc)]),z=(veca.vecc)/([(veca, vecb, vecc)])`
Substituting these values in i we obtain that the given expression is equal to `[(veca, vecb, vecc)]veca`.