Example 2-3-2 - Maple Help

# Online Help

###### All Products    Maple    MapleSim



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 $\mathbf{T}\prime \left(1\right),\mathbf{T}\prime \left(5\right),\mathbf{T}\prime \left(9\right)$.







© Maplesoft, a division of Waterloo Maple Inc., 2021. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.



For more information on Maplesoft products and services, visit www.maplesoft.com