Initialize

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

Define R

$\mathbf{R}≔\mathrm{PositionVector}\left(\left[p \cos \left(p\right)\,p \sin \left(p\right)\right]\right)$

Define F

$\mathbf{F}≔\mathrm{VectorField}\left(⟨x\,y⟩\/\sqrt{x^2\+y^2}\right)$

Use the PlotPositionVector command to obtain the required graph

$\mathrm{PlotPositionVector}\left(\mathbf{R}\,p\=0..2 \mathrm{\π}\, \mathrm{scaling}\=\mathrm{constrained}\,\mathrm{vectorfield}\=\mathbf{F}\,\mathrm{points}\=\left[\mathrm{\pi }\/3\,\mathrm{\pi }\,5 \mathrm{\pi }\/3\right]\,\mathrm{vectorfieldoptions}\=\left[\mathrm{width}\=.15\,\mathrm{color}\=\mathrm{gold}\right]\right)$

Interactive definition of a position vector

$⟨p \cos \left(p\right)\,p \sin \left(p\right)⟩$ = $\stackrel{\text{to position Vector}}{\to }$ $\stackrel{\text{assign to a name}}{\to }$$\mathrm{PV}$$$

$\mathbf{PV}$ = $\stackrel{\text{about}}{\to }$ $$

Interactive definition of a vector field

$\frac{⟨x\,y⟩}{\sqrt{x^2\+y^2}}$ = $\stackrel{\text{to Vector Field}}{\to }$ $\stackrel{\text{assign to a name}}{\to }$$\mathrm{VF}$$$

$\mathbf{VF}$ = $\stackrel{\text{about}}{\to }$ $$

Table 9.2.3(a)   Interactive construction of a position vector and a vector field