If `veca,vecb,vecc` are three non- coplanar vectors and `vecp,vecq,vecr` are vectors defined by the relations `vecp=(vecbxxvecc)/([veca vecb vecc]),vecq=(veccxxveca)/([veca vecb vecc]),vecr=(vecaxxvecb)/([veca vecb vecc]),` then the value of expression `(veca+vecb).vecp+(vecb+vecc).vecq+(vecc+veca).vecr` is equal to

Options

A. 0
B. 1
C. 2
D. 3

Answer

B

Explanation

`veca * vec p + vecb * vecq + vecc * vecr `
`= (veca * vecb xx vec c )/([veca vec b vec c]) + (vec b * vecc xx vec a)/([veca vec b vec c]) + (vec c * vec b xx vec a)/([vec a vec b vec c ])`
`= 1 + 1 - 1 = 1`