Definition:Position Vector/Notation

Notation for Displacement
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.