Chapter 2: Space Curves

Section 2.1: Position-Vector Representation

Example 2.1.5

$$ For $t\in \left[1\,5\right]$, graph the space curve defined parametrically by $x\left(t\right)\=t$, $y\left(t\right)\=\ln \left(t\right)$, $z\left(t\right)\=e^{t\/3}$. On the graph, indicate the points where $t\=1\,3$, and $4$. $$ Solution $$ •  Tools≻Load Package: Student Vector Calculus Loading Student:-VectorCalculus •  Apply the PositionVector command to define the given curve as the position vector R. (Be sure to use the exponential "e".)   •  Press the Enter key. $\mathbf{R}≔\mathrm{PositionVector}\left(\left[t\,\ln \left(t\right)\,{\ⅇ}^{t\/3}\right]\right)$ •  Apply the PlotPositionVector command to graph the curve defined as the position vector R. $\mathrm{PlotPositionVector}\left(\mathbf{R}\mathit{\,}t\=1..5\,\mathrm{points}\=\left[1\,3\,4\right]\,\mathrm{curveoptions}\=\left[\mathrm{labels}\=\left[x\,y\,z\right]\,\mathrm{scaling}\=\mathrm{constrained}\,\mathrm{axes}\=\mathrm{frame}\,\mathrm{tickmarks}\=\left[5\,3\,4\right]\right]\right)$ $$

<< Previous Example   Section 2.1    Next Section >>

© Maplesoft, a division of Waterloo Maple Inc., 2024. 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