Theorem 1: If a and b are two non collinear vectors; then every vector r coplanar with a and b can be expressed in one and only one way as a linear combination: xa+yb.

Options

A. x=0, but y is not necessarily zero
B. y=0, bu tx is not necessarily zero
C. x=0,y=0
D. none of these

Answer

C

Explanation

If a and b are two non-zero, non-collinear vectors and x and y are two scalars such that xa+yb=0 then x=0 and y=0 because one will be a scalar multiple off the other and hence collinear which is a contradiction.