Definition:Unit Tangent 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.

The unit tangent vector of $\alpha$ at $s$ is defined as:
 * $\map t s := \map {\alpha '} s$

where:
 * $\alpha '$ denotes the derivative of $\alpha$