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

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

The ordered pair $\tuple {-y, x}$ can be interpreted as the components of a position vector.

Proof
We use Characteristics of Vector in Plane.

Let:

by setting $V_x = -y$ and $V_y = x$.

From Characteristics of Vector in Plane:

Using Rotation of Cartesian Axes around Vector it is seen that the equalities hold.

Hence the result.