'points'=[a] or 'points'=[[a,b]]

For a position Vector with two parameters, the point [a,b] is interpreted as param1=a and param2= b where param1 and param2 are the parameter names given in the ranges r1 and r2 respectively.

For the point [a], a must lie in the range r and for the point [a,b], a and b must lie in the ranges r1 and r2 respectively. Otherwise, an error message is displayed.

Use [a1,a2,...,ak] or [[a1,b1],...,[ak,bk]] to specify more than one point.

'vectorfield' = VField

Since the position Vector is a Cartesian Vector, the vector field will be converted to Cartesian coordinates before the evaluation.

A list of vector fields can be specified using 'vectorfield'=[VField1,..,VFieldk].

For more information on vector fields, see Student[VectorCalculus][VectorField].

'pvdiff'=[param$k]

More than one derivative can be plotted using 'pvdiff'=[[d1],[d2]...], where each sublist is a valid second argument to diff.

'tangent'= truefalse

'normal'= truefalse

'binormal'= truefalse

'curveoptions' =list

'pointoptions', 'vectorfieldoptions', 'tangentoptions', 'normaloptions', 'binormaloptions' =list

'coordcurve'= [{param1, param2}=a,options1 ]

If the value a of the parameter is out of range, an error message is displayed.

A list of coordinate curves can be specified, using 'coordcurve'=[[...],...,[...]].

'vectorfield' = VField

Since the position Vector is a Cartesian Vector, the vector field will be converted to Cartesian coordinates before the evaluation.

This option can take a list of vector fields, using 'vectorfield'=[VField1,..,VFieldk].

For more information on vector fields, see Student[VectorCalculus][VectorField].

'pvdiff'=[{param1,param2}$k]

More than one derivative can be plotted using 'pvdiff'=[[param$k1],[param$k2]...].

'normal' = truefalse

The orientation of the normal vector can be controlled with the option 'normalorientation'=truefalse.

The formula used to compute the normal vector of a position Vector$\mathit{pv}\left(u,v\right)=x\left(u,v\right)\mathit{i}+y\left(u,v\right)\mathit{j}+z\left(u,v\right)\mathit{k}$ is $\mathit{N}=\frac{\partial \left(y,z\right)}{\partial \left(u,v\right)}\mathit{i}+\frac{\partial \left(z,x\right)}{\partial \left(u,v\right)}\mathit{j}+\frac{\partial \left(x,y\right)}{\partial \left(u,v\right)}\mathit{k}$.

'normalfield' = truefalse

The formula used to compute the normal field of a vector field is $\left(\mathit{N}·\mathit{F}\right)\mathit{N}$ where $\mathit{N}·\mathit{F}$ is the dot product of the normalized normal vector $\mathit{N}$ and  $\mathit{F}$.

'surfaceoptions'=list

'pointoptions', 'diffoptions', 'normaloptions', 'vectorfieldoptions', 'normalfieldoptions'=list;

The PlotPositionVector command plots a curve or surface defined by a two- or three-dimensional position Vector. For a curve, the plot can be in two- or three-dimensional space.

The first argument pv is a position Vector. The components of the position Vector represent the parametric description of the curve or surface in Cartesian coordinates. For more information about position Vectors, see PositionVector.

If the position Vector has one parameter it is assumed to represent a curve.

If the position Vector has two parameters and three components it is assumed to represent a surface. If the position Vector has two parameters and two components it is assumed to represent unevaluated curves.

If the position Vector has no indeterminates, a single Vector rooted at the origin is plotted.

Given a position Vector with one parameter representing a curve, the range r is specified in the form param = a..b or a..b. Given a position Vector with two parameters and three dimensions representing a surface, the ranges r1 and r2 are specified in the form param1=a..b and param2=c..d respectively. Given a position Vector with two parameters and two components, one parameter has to be assigned a specific value and the other must be a range of the form param = a..b.

The optional arguments options1 and options2 provide plot options and control extra structures that can be added to the plot of the curve and surface.

Use PlotVector to plot vector fields, free Vectors, and rooted Vectors.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right)\:$

$\mathrm{pv1}≔\mathrm{PositionVector}\left(\left[1\,2\,3\right]\,\mathrm{cartesian}\left[x,y,z\right]\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{pv1}\right)$

$\mathrm{R1}≔\mathrm{PositionVector}\left(\left[p\,p^2\right]\,\mathrm{polar}\left[r,t\right]\right)$

$\mathrm{R1}≔\left[\begin{array}{c}p\cos \left(p^2\right)\\ p\sin \left(p^2\right)\end{array}\right]$

$\mathrm{PlotPositionVector}\left(\mathrm{R1}\,p=1..2\right)$

$\mathrm{R2}≔\mathrm{PositionVector}\left(\left[v\,v\right]\,\mathrm{polar}\left[r,\mathrm{\theta }\right]\right)$

$\mathrm{R2}≔\left[\begin{array}{c}v\cos \left(v\right)\\ v\sin \left(v\right)\end{array}\right]$

$\mathrm{PlotPositionVector}\left(\mathrm{R2}\,0..3\mathrm{\pi }\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{R2}\,v=0..3\mathrm{\pi }\,\mathrm{tangent}=\mathrm{true}\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{R2}\,v=0..3\mathrm{\pi }\,\mathrm{tangent}=\mathrm{true}\,\mathrm{pvdiff}=\left[v\right]\right)$

$\mathrm{VF1}≔\mathrm{VectorField}\left(⟨-x\,-y⟩\,\mathrm{cartesian}\left[x,y\right]\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{R2}\,v=0..3\mathrm{\pi }\,\mathrm{vectorfield}=\mathrm{VF1}\right)$

$\mathrm{R3}≔\mathrm{PositionVector}\left(\left[1\,\frac{\mathrm{\pi }}{2}+\arctan \left(\frac{1}{2}t\right)\,t\right]\,\mathrm{spherical}\right)$

$\mathrm{R3}≔\left[\begin{array}{c}\frac{2\cos \left(t\right)}{\sqrt{t^2+4}}\\ \frac{2\sin \left(t\right)}{\sqrt{t^2+4}}\\ -\frac{t}{\sqrt{t^2+4}}\end{array}\right]$

$\mathrm{PlotPositionVector}\left(\mathrm{R3}\,t=0..4\mathrm{\pi }\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{R3}\,t=0..4\mathrm{\pi }\,\mathrm{tangent}=\mathrm{true}\,\mathrm{normal}=\mathrm{true}\,\mathrm{binormal}=\mathrm{true}\right)$

$\mathrm{VF2}≔\mathrm{VectorField}\left(⟨r\,0\,0⟩\,\mathrm{spherical}\left[r,p,t\right]\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{R3}\,t=0..4\mathrm{\pi }\,\mathrm{vectorfield}=\mathrm{VF2}\,\mathrm{vectornum}=6\right)$

$\mathrm{R4}≔\mathrm{PositionVector}\left(\left[1\,p\,p\right]\,\mathrm{cylindrical}\left[r,p,s\right]\right)$

$\mathrm{R4}≔\left[\begin{array}{c}\cos \left(p\right)\\ \sin \left(p\right)\\ p\end{array}\right]$

$\mathrm{PlotPositionVector}\left(\mathrm{R4}\,p=0..4\mathrm{\pi }\,\mathrm{tangent}=\mathrm{true}\,\mathrm{points}=\left[\mathrm{\pi }\right]\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{R4}\,p=0..4\mathrm{\pi }\,\mathrm{tangent}=\mathrm{true}\,\mathrm{normal}=\mathrm{true}\,\mathrm{binormal}=\mathrm{true}\,\mathrm{points}=\left[\mathrm{\pi }\,\frac{\mathrm{\pi }}{2}\right]\right)$

$\mathrm{pv2}≔\mathrm{PositionVector}\left(\left[p\,q\right]\,\mathrm{polar}\left[r,t\right]\right)$

$\mathrm{pv2}≔\left[\begin{array}{c}p\cos \left(q\right)\\ p\sin \left(q\right)\end{array}\right]$

$\mathrm{PlotPositionVector}\left(\mathrm{pv2}\,p=1..2\,q=\frac{\mathrm{\pi }}{4}\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{pv2}\,p=2\,q=0..\mathrm{\pi }\right)$

$\mathrm{S1}≔\mathrm{PositionVector}\left(\left[t\,\frac{v}{\mathrm{sqrt}\left(1+t^2\right)}\,\frac{vt}{\mathrm{sqrt}\left(1+t^2\right)}\right]\,\mathrm{cartesian}\left[x,y,z\right]\right)$

$\mathrm{S1}≔\left[\begin{array}{c}t\\ \frac{v}{\sqrt{t^2+1}}\\ \frac{vt}{\sqrt{t^2+1}}\end{array}\right]$

$\mathrm{PlotPositionVector}\left(\mathrm{S1}\,t=-3..3\,v=-3..3\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{S1}\,t=-3..3\,v=-3..3\,\mathrm{points}=\left[\left[0\,0\right]\,\left[1\,1\right]\,\left[2\,2\right]\,\left[3\,3\right]\right]\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{S1}\,t=-3..3\,v=-3..3\,\mathrm{pvdiff}=\left[\left[t\right]\,\left[v\right]\right]\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{S1}\,t=-3..3\,v=-3..3\,\mathrm{vectorfield}=\mathrm{VectorField}\left(⟨x\,y\,0⟩\,\mathrm{cartesian}\left[x,y,z\right]\right)\,\mathrm{vectorgrid}=\left[3\,3\right]\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{PositionVector}\left(\left[x\,y\,x^2{y}^2\right]\right)\,x=-1..1\,y=-1..1\,\mathrm{coordcurve}=\left[\left[x=\frac{1}{2}\,\mathrm{tangent}=\mathrm{true}\,\mathrm{normal}=\mathrm{true}\,\mathrm{vectornum}=2\,\mathrm{tangentoptions}=\left[\mathrm{color}=\mathrm{red}\right]\right]\,\left[x=-1\,\mathrm{tangent}=\mathrm{true}\,\mathrm{vectornum}=2\right]\right]\,\mathrm{scaling}=\mathrm{constrained}\,\mathrm{axes}=\mathrm{frame}\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{S1}\,t=-3..3\,v=-3..3\,\mathrm{vectorfield}=\mathrm{VectorField}\left(⟨x\,y\,0⟩\,\mathrm{cartesian}\left[x,y,z\right]\right)\,\mathrm{normalfield}=\mathrm{true}\right)$

$\mathrm{S2}≔\mathrm{PositionVector}\left(\left[1\,p\,q\right]\,\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)$

$\mathrm{S2}≔\left[\begin{array}{c}\sin \left(p\right)\cos \left(q\right)\\ \sin \left(q\right)\sin \left(p\right)\\ \cos \left(p\right)\end{array}\right]$

$\mathrm{PlotPositionVector}\left(\mathrm{S2}\,p=0..\frac{\mathrm{\pi }}{2}\,q=0..2\mathrm{\pi }\,\mathrm{vectorfield}=\mathrm{VectorField}\left(⟨r\,0\,0⟩\,\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)\,\mathrm{surfaceoptions}=\left[\mathrm{color}=\mathrm{red}\right]\right)$

$\mathrm{PlotPositionVector}\left(\mathrm{S2}\,p=0..\frac{\mathrm{\pi }}{2}\,q=0..2\mathrm{\pi }\,\mathrm{coordcurve}=\left[p=\frac{\mathrm{\pi }}{4}\,\mathrm{curveoptions}=\left[\mathrm{color}='\mathrm{green}'\,\mathrm{thickness}=5\right]\,\mathrm{vectorfield}=\mathrm{VectorField}\left(⟨r\,0\,0⟩\,\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)\right]\,\mathrm{surfaceoptions}=\left[\mathrm{scaling}=\mathrm{constrained}\right]\right)$