Editing Position (geometry) (section)

{{short description|Vector representing the position of a point with respect to a fixed origin}}
[[File:Radius vector - position vector - ortsvektor - radijvektor.svg|thumb|Radius vector <math>\vec{r}</math> represents the position of a point <math>\mathrm{P}(x,y,z)</math> with respect to origin O. In Cartesian coordinate system <math>\vec{r}=x\,\hat{e}_x+y\,\hat{e}_y+z\,\hat{e}_z.</math>]]

In [[geometry]], a '''position''' or '''position vector''', also known as '''location vector''' or '''radius vector''', is a [[Euclidean vector]] that represents a [[Point (geometry)|point]] ''P'' in [[space]]. Its length represents the distance in relation to an arbitrary reference [[origin (mathematics)|origin]] ''O'', and its [[Direction (geometry)|direction]] represents the angular orientation with respect to given reference axes. Usually denoted '''x''', '''r''', or '''s''', it corresponds to the straight line segment from ''O'' to ''P''.
In other words, it is the [[displacement (vector)|displacement]] or [[translation (geometry)|translation]] that maps the origin to ''P'':<ref>The term ''displacement'' is mainly used in mechanics, while ''translation'' is used in geometry.</ref>

:<math>\mathbf{r}=\overrightarrow{OP}.</math>

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 space]]s and [[affine space]]s of any [[dimension]].<ref name="phys_keller">Keller, F. J., Gettys, W. E. et al. (1993), p.&nbsp;28–29.</ref>