Definition:Position Vector/Notation

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.

Sources

• 1927: C.E. Weatherburn: Differential Geometry of Three Dimensions: Volume $\text { I }$ ... (previous) ... (next): Introduction: Vector Notation and Formulae
• 1957: D.E. Rutherford: Vector Methods (9th ed.) ... (previous) ... (next): Chapter $\text I$: Vector Algebra: $\S 9$
• 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach: $(1.3)$