Initialize

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

Define R

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

Define F

$\mathbf{F}≔\mathrm{VectorField}\left(⟨y z\,x z\, x y⟩\right)$

Use the PlotPositionVector command, applying the Normalize command to F

$\mathrm{PlotPositionVector}\left(\mathbf{R}\,x\=-1..1\,y\=-1..1\,\mathrm{scaling}\=\mathrm{constrained}\,\mathrm{axes}\=\mathrm{frame}\,\mathrm{labels}\=\left[x\,y\,z\right]\,\mathrm{vectorfield}\=\mathrm{Normalize}\left(\mathbf{F}\right)\,\mathrm{vectorfieldoptions}\=\left[\mathrm{color}\=\mathrm{gold}\right]\,\mathrm{points}\=\left[\left[.5\,.5\right]\,\left[-.5\,-.5\right]\right]\,\mathrm{normalfield}\=\mathrm{true}\,\mathrm{normalfieldoptions}\=\left[\mathrm{color}\=\mathrm{black}\right]\,\mathrm{tickmarks}\=\left[3\,3\,2\right]\,\mathrm{orientation}\=\left[-45\,65\,0\right]\right)$

Interactive definition of a position vector

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

Interactive definition of a vector field

$⟨y z\,x z\,x y⟩$ = $\stackrel{\text{to Vector Field}}{\to }$ $\stackrel{\text{about}}{\to }$

Table 9.2.5(a)   Interactive construction of a position vector and a vector field