Example 2-3-2 - Maple Help



Chapter 2: Space Curves



Section 2.3: Tangent Vectors



Example 2.3.2



If $\mathbf{R}\left(p\right)$ is the position-vector representation of $C$, the parametric curve , , ,

 a) Obtain $\mathrm{ρ}=∥\mathbf{R}\prime \left(p\right)∥$ and the unit tangent vector $\mathbf{T}=\mathbf{R}\prime /\mathrm{ρ}$.
 b) Graph R and the vectors $\mathbf{R}\prime \left(1\right),\mathbf{R}\prime \left(5\right),\mathbf{R}\prime \left(9\right)$ along $C$.
 c) Graph R and the vectors $\mathbf{T}\left(1\right),\mathbf{T}\left(5\right),\mathbf{T}\left(9\right)$ along $C$.
 d) Show that $\mathbf{T}·\mathbf{T}\prime \left(p\right)=0$, thus verifying that a unit vector is necessarily orthogonal to its derivative.
 e) To the graph in Part (c), add the vectors $\mathbf{T}\prime \left(1\right),\mathbf{T}\prime \left(5\right),\mathbf{T}\prime \left(9\right)$.