If `veca, vecb, vecc` are three non-coplanar vectors, then a vector `vecr` satisfying `vecr.veca=vecr.vecb=vecr.vecc=1`, is

Options

A. `vecaxxvecb+vecbxxvecc+veccxxveca`
B. `1/([(veca, vecb, vecc)]){vecaxxvecb+vecbxxvec+veccxxveca}`
C. `[(veca, vecb, vecc)]{vecaxxvecb+vecbxxvecc+vecxxveca}`
D. none of these

Answer

B

Explanation

Since `veca, vecb, vecc` are three non-coplanar vectors.
Therefore `vecaxxvecb, vecbxxvecc` and `veccxxveca` are also non coplanar vectors.
Let `vecr=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca)`. Then,
`vecr.veca=1implies1=y{((vecbxxvecc).veca)}impliesy=1/([(veca, vecb, vecc)])`
Similarly `vecr.vecb=1` and `vecr.vecc=1` will give
`z=1/([(veca, vecb, vecc)])` and `x=1/([(veca, vecb, vecc)])`
Hence `vecr=1/([(veca, vecb, vecc)]){vecaxxvecb+vecbxxvecc+veccxxveca}` is the required solution.