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If a and b are two non collinear vectors...

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=0.

A

(a)x=0, but y is not necessarily zero

B

(b)y=0, but x is not necessarily zero

C

(c)x=0,y=0

D

(d)none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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.
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