Let a,b,c be three vectors such that [a b c]=2, if `r=l(bxxc)+m(cxxa)+n(axxb)` is perpendicular to a+b+c, 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`