# Definition:Positive Unit Normal

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## Definition

Let $S$ be a surface in ordinary $3$-space.

### Closed Surface

A **positive unit normal** to $S$ is a unit normal $\mathbf {\hat n}$ to $S$ at a point $P$ on $S$ such that the terminal point of $\mathbf {\hat n}$ is on the exterior of $S$.

That is, it is constructed **outwards** from the enclosed region of space.

### Unclosed Surface

A **positive unit normal** to $S$ is a unit normal $\mathbf {\hat n}$ to $S$ whose direction is arbitrarily defined, but usually such that it is generally away from the origin of whatever coordinate system is being used.

## Sources

- 1951: B. Hague:
*An Introduction to Vector Analysis*(5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $3$. Line and Surface Integrals