Definition:Binormal Vector of Curve Parameterized by Arc Length/3-Dimensional Real Vector Space

Definition
Let $\alpha : I \to \R^3$ be a smooth curve parameterized by arc length.

Let $s \in I$ be such that the curvature $\map \kappa s \ne 0$.

The binormal vector of $\alpha$ at $s$ is defined as:
 * $\map b s := \map t s \times \map n s$

where:
 * $\map t s$ is the unit tangent vector
 * $\map n s$ is the normal vector
 * $\times$ denotes the vector cross product