In mathematics, the term vector generally refers to a * geometric vector*.

In a Cartesian plane, a geometric vector is represented by an arrow or a directed line segment.

In this case, \(\overrightarrow {u}\) is represented by an arrow from point \(\overrightarrow {v}\) is a vector with a length of \(2\sqrt {5}\).

A geometric vector \(\overrightarrow {AB}\) is represented by an arrow from point *A* towards point *B*. Every pair of points equivalent to (A, B) can be used to define an arrow of the same vector. Therefore, a vector is considered to be an infinite set of pairs of points equivalent to a given pair of points.