# Definition:Del Operator/Cartesian 3-Space

## Definition

Let $\R^3$ be a Cartesian $3$-space.

Let $\tuple {\mathbf i, \mathbf j, \mathbf k}$ be the standard ordered basis on $\R^3$.

The del operator is defined in $\R^3$ as:

$\operatorname {del} = \nabla := \mathbf i \dfrac \partial {\partial x} + \mathbf j \dfrac \partial {\partial y} + \mathbf k \dfrac \partial {\partial z}$