Definition:Position Vector/Notation

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Notation for Position Vector

When considering a position 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 $\mathbf k$ are unit vectors along the $x$-axis, $y$-axis and $z$-axis from $O$ respectively.