Definition:Unit Normal

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

Let $P$ be a point of $S$.

Let $\mathbf n$ be a normal to $S$ at $P$ such that $\mathbf n$ is a unit vector.

Then $\mathbf n$ is known as a unit normal.

Also known as

It is a popular convention to use the hat notation for a unit vector, hence $\mathbf {\hat n}$ can often be seen to denote a unit normal.