In order to describe the motion of an object, you must first be able to describe its **position** (where it is at any particular time). More precisely, you need to specify its position relative to a convenient reference frame.

So the position of a point \(P\) can be described by a pair or a set of coordinates, such as: \(P=(x, y)\) (in two dimensions) or \(P=(x, y, z)\) (in three dimensions).

## Position vector

The **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 \(\vec{r}\), or \(\vec{s}\), it corresponds to the straight-line from \(O\) to \(P\).

In other words, it is the displacement or translation that maps the origin to \(P\). In one dimension \(x(t)\) is used to represent position as a function of time. In two dimensions, either cartesian or polar coordinates may be used, and the use of unit vectors is common. A position vector \(r\) may be expressed in terms of the unit vectors as follow:

\[\vec{r}(t)=x\vec{i}+y\vec{j}\]

In three dimensions, cartesian or spherical polar coordinates are used, as well as other coordinate systems for specific geometries.

\[\vec{r}(t)=x\vec{i}+y\vec{j}+z\vec{k}\]

The vector change in position associated with a motion is called the displacement.