# 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:

$\mathbf {r} ={\overrightarrow {OP}}$  Radius vector r → {\displaystyle {\vec {r}}} represents the position of a point P ( x , y , z ) {\displaystyle \mathrm {P} (x,y,z)} with respect to origin O. In Cartesian coordinate system r → = x e ^ x + y e ^ y + z e ^ z {\displaystyle {\vec {r}}=x\,{\hat {e}}_{x}+y\,{\hat {e}}_{y}+z\,{\hat {e}}_{z}} .

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.