Let `veca, vecb, vecc` be three vectors such that `[(veca, vecb, vecc)]=2`. If `vecr=l(vecbxxvecc)+m(veccxxveca)+n(vecaxxvecb)` be perpendicular to `veca+vecb+vecc` , then the value of `l+m+n` is

Options

A. 2
B. 1
C. 0
D. none of these

Answer

C

Explanation

It is given that `vecr` perpendicular `(veca+vecb+vecc)`
`:.vecr.(veca+vecb+vecc)=0`
`=l[(veca, vecb, vecc)]+m[(vecc, veca, vecc)]+[(veca, vecb, vecc)]=0`
`implies2(l+m+n)=0[ :'[(veca, vecb, vecc)]=2]`
`impliesl+m+n=0`