Page "Euclidean vector" Paragraph 16

However, it is not always possible or desirable to define the length of a vector in a natural way.

This more general type of spatial vector is the subject of vector spaces ( for bound vectors ) and affine spaces ( for free vectors ).

An important example is Minkowski space that is important to our understanding of special relativity, where there is a generalization of length that permits non-zero vectors to have zero length.

Other physical examples come from thermodynamics, where many of the quantities of interest can be considered vectors in a space with no notion of length or angle.