# Definition:Displacement

## Definition

The (physical) displacement of a body is a measure of its position relative to a given point of reference in a particular frame of reference.

Displacement is a vector quantity, so it specifies a magnitude and direction from the point of reference.

In Cartesian coordinates, the direction is implicit, as it occurs as a result of the combined distances from the various axes of the frame of reference.

### Notation

When considering a displacement vector $\mathbf r$ with respect to the origin $O$ of a point $P$ in space under a Cartesian coordinate system, it is commonplace to refer to it as:

$P = \tuple {x, y, z}$

where $x$, $y$ and $z$ are the components of $\mathbf r$ in the directions of the coordinate axes.

Hence $P = \tuple {x, y, z}$ can be regarded as shorthand for:

$\mathbf r = x \mathbf i + y \mathbf j + z \mathbf k$

where $\mathbf i$, $\mathbf j$ and $\mathbf i$ are unit vectors along the $x$-axis, $y$-axis and $z$-axis from $O$ respectively.

### Dimension

The dimension of displacement is length $\mathsf L$.

### SI

The SI unit of displacement is the metre.

### CGS

The CGS unit of displacement is the centimetre $\mathrm {cm}$.

### FPS

The FPS unit of displacement is the foot $\mathrm f$.

## Also known as

The displacement of a body is also known as its position vector.