If `veca, vecb, vecc` are non coplanar vectors and `vecp, vecq, vecr` are reciprocal vectors, then
`(lveca+mvecb+nvecc).(lvecp+mvecq+nvecr)` is equal to

Options

A. `l^(2)+m^(2)+n^(2)`
B. lm+mn+nl
C. 0
D. None of these

Answer

A

Explanation

The vectors reciprocal to `veca,vecb,vecc`, are given by `vecp=(vecb xx vecc)/[vecavecbvecc], vecq= (vecc xx veca)/[vecavecbvecc], vecr = (veca xx vecb)/([vecavecbvecc])`such that `veca.vecp=1, veca.vecq=veca.vecr=0`,
`vecb.vecq=1, vecb.vecp=vecb.vecr=0`
`vecc.vecr=1, vecc. vecp=vecc.vecq=0`
This gives `(lveca+mvecb+nvecc).(lvecp+mvecq+nvecr)`
`=l^(2)+m^(2)+n^(2)`.