# Decomposition of a vector in a plane

## Theorem

If and be any two non-zero and non-collinear vectors then any vector in the plane of and can be uniquely expressed as the sum of two vectors parallel to the vectors and .
and be any two non-zero and non-collinear plane vectors. Let be any other vector in the plane of the vectors and . Now from the point P draw the straight lines PG and PH parallel to the lines OA and OB as shown in the succeeding figure below.

**Proof:**Let## New Resources

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