Example 2-3-5 - Maple Help



Chapter 2: Space Curves



Section 2.3: Tangent Vectors



Example 2.3.5



 If $\mathbf{R}\left(s\right)$ is the position vector for $C$, a curve parametrized by $s$, the arc length, and $\mathbf{T}\left(s\right)=\mathbf{R}\prime \left(s\right)$ is the unit tangent vector along $C$, show that $\mathbf{T}\mathbf{·}\mathbf{T}\prime =0$, thereby proving that the unit tangent vector is necessarily orthogonal to its derivative.