\begin{definition}[Definition:Del Operator/Cartesian 3-Space]
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:
:$\operatorname {del} = \nabla := \mathbf i \dfrac \partial {\partial x} + \mathbf j \dfrac \partial {\partial y} + \mathbf k \dfrac \partial {\partial z}$
\end{definition}