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Coordinate Systems and Frames of Reference

The location of a point on a line can be described by one coordinate; a point on a plane can be described by two coordinates; a point in a three dimensional volume can be described by three coordinates. In general, the number of coordinates equals the number of dimensions. A coordinate system consists of:

a fixed reference point (origin)
a set of axes with specified directions and scales
instructions that specify how to label a point in space relative to the origin and axes.

For Example:

Definition: The position vector ( $\vec{r}$ ) in any given coordinate system specifys the position of a given point within that coordinate system relative to the origin.