Two vectors a and b are collinear if there exists a number n such that

      a = n.b

=> a - n.b = 0

So we can always find a linear combination of collinear vectors a, b that combines to 0

If we have two vectors which are not collinear then the only way we can combine them linearly

to make 0 is to use the coefficient of 0.

i.e.  0.a + 0.b = 0  ( both coefficients are 0)