`veca, vecb ,vecc` are three non zero vectors no two of which are collonear and the vectors `veca + vecb` be collinear with `vecc,vecb+vecc` to collinear with `veca` then `veca+vecb+vecc` the equal to ? (A) `veca` (B) `vecb` (C) `vecc` (D) None of these

Explanation

As `veca+vecb` is collinear with `vec c`,

`:. veca+vecb = lambda vecc->(1)`

As `vecb+vecc` is collinear with `vec a`,

`:. vecb+vecc = gamma veca`

From (1),

`=>vecb + (veca+vecb)/lambda = gamma veca`

`=>vecb (1+1/lambda) = veca(gamma - 1/lambda)`

As `(1+1/lambda)` and `(gamma - 1/lambda)` are constant, we can write the above equation as,

...