Characteristics of Vector in Plane/Examples/x, -y

Examples of Use of Characteristics of Vector in Plane
Let a Cartesian plane $\CC$ be established with origin $O$.

The ordered pair $\tuple {x, -y}$ cannot be interpreted as the components of a position vector.

Proof
We use Characteristics of Vector in Plane.

Let:

These equations are inconsistent with Characteristics of Vector in Plane.