Chapter 2: Space Curves

Section 2.1: Position-Vector Representation

Example 2.1.4

$$ For $t\in \left[0\,3 \mathrm{\π}\right]$, graph the helix defined parametrically by $x\left(t\right)\=\cos \left(t\right)$, $y\left(t\right)\=\sin \left(t\right)$, $z\left(t\right)\=t\/3$. On the graph, indicate the points where $t\=\mathrm{\π}$, and $2 \mathrm{\π}$. $$ Solution $$ •  Tools≻Load Package: Student Vector Calculus Loading Student:-VectorCalculus •  Apply the PositionVector command to define the given curve as the position vector R.   •  Press the Enter key. $\mathbf{R}≔\mathrm{PositionVector}\left(\left[\cos \left(t\right)\,\sin \left(t\right)\,t\/3\right]\right)$ •  Apply the PlotPositionVector command to graph the curve defined as the position vector R. $\mathrm{PlotPositionVector}\left(\mathbf{R}\mathit{\,}t\=0..3 \mathrm{\π}\,\mathrm{points}\=\left[\mathrm{\π}\,2 \mathrm{\π}\right]\,\mathrm{curveoptions}\=\left[\mathrm{labels}\=\left[x\,y\,z\right]\,\mathrm{scaling}\=\mathrm{constrained}\,\mathrm{axes}\=\mathrm{frame}\,\mathrm{tickmarks}\=\left[3\,3\,3\right]\right]\right)$ $$

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