Normal Vector

Definition: Normal Vector

Let $\gamma :I\subseteq \mathbb{R}\to {\mathbb{R}}^n$ be a parametric curve whose unit tangent vector $\mathbf{T}$ is differentiable at $t\in I$.

The derivative $\dot{\mathbf{T}}(t)$ of $\mathbf{T}$ is known as $\gamma$‘s normal vector at $t$.

Definition: Unit Normal Vector

The unit normal vector is the unit vector obtained from $\gamma$‘s normal vector:

$$\frac{1}{||\dot{\mathbf{T}}(t)||}\dot{\mathbf{T}}(t)$$

NOTATION

$$\mathbf{N}(t)$$