Definition:Area Element/Outward Normal

Definition
Let $\delta \mathbf S$ be an area element embedded in a coordinate frame with position vector $\mathbf r$.

The outward normal of $\delta \mathbf S$ is defined to be the normal vector $\mathbf n$ to $\delta \mathbf S$ such that:
 * $\mathbf r \cdot \mathbf n > 0$

where $\cdot$ denotes the dot product.

In the event that $\mathbf r \cdot \mathbf n = 0$, the outward normal may be chosen arbitrarily.