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

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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:

\(\ds {V'}_x\) \(=\) \(\ds x'\) \(\ds = x \cos \varphi - y \sin \varphi\)
\(\ds {V'}_y\) \(=\) \(\ds -y'\) \(\ds = -x \sin \varphi - y \cos \varphi\)

These equations are inconsistent with Characteristics of Vector in Plane.


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