# Position Vector

(Redirected from Displacement Vector)

A Position Vector is an Euclidean vector which corresponds distances along each axis of the reference frame from the origin to the location of a given point, particle or physical body.

$\hat{\boldsymbol e_r} =\sin \theta \cos \varphi \,\hat{\boldsymbol e_x} + \sin \theta \sin \varphi \,\hat{\boldsymbol e_y} + \cos \theta \,\hat{\boldsymbol e_z}$
$\hat{\boldsymbol e_\theta} =\cos \theta \cos \varphi \,\hat{\boldsymbol e_x} + \cos \theta \sin \varphi \,\hat{\boldsymbol e_y} -\sin \theta \,\hat{\boldsymbol e_z}$
$\hat{\boldsymbol e_\varphi} =-\sin \varphi \,\hat{\boldsymbol e_x} + \cos \varphi \,\hat{\boldsymbol e_y}$

## References

### 2016

• (Wikipedia, 2016) ⇒ https://www.wikiwand.com/en/Position_(vector) Retrieved:2016-5-22.
• 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 distances along each axis from O to P:
$r=\overrightarrow{OP}.$
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 in any number of dimensions