= Normal line to a plane curve
At a regular point of a differentiable <plane curve>, the normal line passes through that point perpendicular to its <tangent line>. If the tangent slope is a finite nonzero number $m$, the normal slope is $-1/m$, since the direction vectors $(1,m)$ and $(1,-1/m)$ have zero <dot product>. A horizontal tangent has a vertical normal, and a vertical tangent has a horizontal normal. For a regular <level set> $F(x,y)=c$, the nonzero <gradient> $\nabla F$ gives a normal direction because differentiating $F$ along the curve gives $\nabla F\cdot\mathbf r'=0$.
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