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

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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


Sources