Definition:Positive Unit Normal

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Definition

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


Closed Surface

Let $S$ be closed in space.

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

Let $S$ be unclosed in space.

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.


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