Position (geometry)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P. In other words, it is the displacement or translation that maps the origin to P:[1]

${\displaystyle \mathbf {r} ={\overrightarrow {OP}}}$

The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.

Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces and affine spaces of any dimension.[2]