Editing Position (geometry) (section)

===Three dimensions===

[[File:Space curve.svg|thumb|[[Space curve]] in 3D. The [[position vector]] '''r''' is parameterized by a scalar ''t''. At '''r''' = '''a''' the red line is the tangent to the curve, and the blue plane is normal to the curve.]]

In [[three dimensions]], any set of three-dimensional coordinates and their corresponding basis vectors can be used to define the location of a point in space—whichever is the simplest for the task at hand may be used.

Commonly, one uses the familiar [[Cartesian coordinate system]], or sometimes [[spherical polar coordinates]], or [[cylindrical coordinate system|cylindrical coordinates]]:

:<math> \begin{align} 
 \mathbf{r}(t) 
 & \equiv \mathbf{r}(x,y,z) \equiv x(t)\mathbf{\hat{e}}_x + y(t)\mathbf{\hat{e}}_y + z(t)\mathbf{\hat{e}}_z  \\
 & \equiv \mathbf{r}(r,\theta,\phi) \equiv r(t)\mathbf{\hat{e}}_r\big(\theta(t), \phi(t)\big) \\
 & \equiv \mathbf{r}(r,\phi,z) \equiv r(t)\mathbf{\hat{e}}_r\big(\phi(t)\big) + z(t)\mathbf{\hat{e}}_z, \\
\end{align}</math>

where ''t'' is a [[parametric equation|parameter]], owing to their rectangular or circular symmetry. These different coordinates and corresponding basis vectors represent the same position vector. More general [[curvilinear coordinates]] could be used instead and are in contexts like [[continuum mechanics]] and [[general relativity]] (in the latter case one needs an additional time coordinate).