Initialize

$$\begin{gathered} \mathrm{with}\left(\mathrm{Student}:-\mathrm{VectorCalculus}\right)\: \\ \mathrm{BasisFormat}\left(\mathrm{false}\right)\: \end{gathered}$$

Define R

$\mathbf{R}≔\mathrm{PositionVector}\left(\left[x\,y\,x^2{y}^2\right]\right)$

Use the PlotPositionVector command to obtain the required graph

$\mathrm{PlotPositionVector}\left(\mathbf{R}\,x\=-1..1\,y\=-1..1\,\mathrm{coordcurve}\=\left[\left[x\=1\/2\,\mathrm{tangent}\=\mathrm{true}\,\mathrm{normal}\=\mathrm{true}\,\mathrm{binormal}\=\mathrm{true}\,\mathrm{vectornum}\=2\,\mathrm{tangentoptions}\=\left[\mathrm{color}\=\mathrm{red}\right]\right]\,\left[y\=-1\,\mathrm{tangent}\=\mathrm{true}\,\mathrm{vectornum}\=2\right]\right]\,\mathrm{scaling}\=\mathrm{constrained}\,\mathrm{axes}\=\mathrm{frame}\,\mathrm{labels}\=\left[x\,y\,z\right]\,\mathrm{orientation}\=\left[-35\,60\,0\right]\,\mathrm{tickmarks}\=\left[3\,3\,3\right]\right)$

Interactive definition of a position vector

$⟨x\,y\,x^2{y}^2⟩$ = $\stackrel{\text{to position Vector}}{\to }$ $\stackrel{\text{about}}{\to }$

Table 9.2.4(a)   Interactive construction of a position vector