Editing Euclidean vector (section)

===Length and units===
In abstract vector spaces, the length of the arrow depends on a [[Dimensionless number|dimensionless]] [[Scale (measurement)|scale]]. If it represents, for example, a force, the "scale" is of [[Dimensional analysis|physical dimension]] length/force. Thus there is typically consistency in scale among quantities of the same dimension, but otherwise scale ratios may vary; for example, if "1 newton" and "5 m" are both represented with an arrow of 2&nbsp;cm, the scales are 1 m:50 N and 1:250 respectively. Equal length of vectors of different dimension has no particular significance unless there is some [[proportionality constant]] inherent in the system that the diagram represents. Also length of a unit vector (of dimension length, not length/force, etc.) has no coordinate-system-invariant significance.