If the vectors `veca, vecb, vecc` are non -coplanar and `l,m,n` are distinct scalars such that
`[(lveca+mvecb+nvecc, lvecb+mvecc+nveca,lvecc+mveca+nvecb)]=0` then

Options

A. `lm+mn+nl=0`
B. `l+m+n=0`
C. `l^(2)+m^(2)+n^(2)=0`
D. `l^(3)+m^(3)+n^(3)=0`

Answer

B

Explanation

We have `[(lveca+mvecb+nvecc,lvecb+mvecc+nveca,lvecc+mveca+nvecb)]=0`
`implies[(lveca+mvecb+nvecc,nveca+lvecb+mvecc,mveca+nvecb+lvecc)]=0` ltbgt `implies|(l,m,n),(n,l,m),(m,m,l)|=[(veca, vecb, vecc)]=0`
`implies|(l,m,n),(n,l,m),(m,n,l)|=0 [ :' [(veca, vecb, vecc)]!=0]`
`=l^(3)+m^(3)+n^(3)-3lmn=0`
`implies(l+m+n)(l^(2)+m^(2)-lm-mn-nl)=0`
`impliesl+m+n=0`