Normal vector

A normal vector is orthogonal to every tangent vector in the tangent space.

A unit normal is a normal vector of norm one.

Relative to a unit normal $\mathbf{n}$, a vector $\mathbf{v}$ decomposes orthogonally asThe first term is its normal component and the second its tangential component.

The normal derivative of a differentiable function $u$ along a hypersurface with unit normal $N$ is the directional derivativeHigher normal derivatives at a point $x$ may be defined by differentiating the one-variable function $s\mapsto u(x+sN(x))$ repeatedly at $s=0$.