Three non-zero vectors `vec(a), vec(b), vec(c)` are such that no two of them are collinear. If the vector `(vec(a)+vec(b))` is collinear with the vector `vec(c)` and the vector `(vec(b)+vec(c))` is collinear with vector `vec(a)`, then prove that `(vec(a)+vec(b)+vec(c))` is a null vector.