# Position (geometry)

## Vector representing the position of a point with respect to a fixed origin / From Wikipedia, the free encyclopedia

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In geometry, a **position** or **position vector**, also known as **location vector** or **radius vector**, is a Euclidean vector that represents a point *P* in space. Its length represents the distance in relation to an arbitrary reference origin *O*, and its 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 or translation that maps the origin to *P*:^{[1]}

- $\mathbf {r} ={\overrightarrow {OP}}.$

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]}