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Concept# Position (geometry)

Summary

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}
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.
Relative position
Directed line segment
The relative position of a point Q with respect to point P is the Euclidean vector resulting from the subtraction of the two absolute position vectors (each with respect to the origin):
:\Delta \mathbf{r}=\mathbf{s} - \mathbf{r}=\ove

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