If ` vec a ,\ vec b ,\ vec c` are three non-zero vectors, no two f thich are collinear and the vector ` vec a+ vec b` is collinear with ` vec c ,\ vec b+ vec c` is collinear with ` vec a ,\ t h e n\ vec a+ vec b+ vec c=` ` vec a` b. ` vec b` c. ` vec c` d. none of these

Options

A. A
B. B
C. C
D. 0

Answer

D

Explanation

Since, A + B is collinear to C and B + C is collinear to A.
`therefore A + B = lambda C`
and `B + C = mu A`
where, `lambda` and `mu` are scalars.
`implies A+B+C=(lambda+1)C`
and `A+B+C=(mu+1)A`
`implies (lambda+1)C=(mu+1)A`
If `lambda ne-1`, then
`C=(mu+1)/(lambda+1)A`
implies C and A are collinear.
This is a contradiction to the given condition.
`therefore lambda = - 1`
`therefore A + B + C = 0`