Plotting

In[130]:=

  ?PlotVectorField

  PlotVectorField[f, {x, x0, x1, (xu)}, {y, y0, y1, (yu)},

     (options)] produces a vector field plot of the

     two-dimensional vector function f.

In[131]:=

  PlotVectorField[{x y,x-y},{x,-3,3},{y,-3,3}];

Think of fluid flow. The vectors represent the flow of the fluid at the tail of the vector. The length of the vector represents the speed of the flow and the direction of the vector represents the direction of the flow.

In[132]:=

  ?PlotVectorField3D

  PlotVectorField3D[{xfunc,yfunc,zfunc},xrange,yrange,zrange]

     plots a vector field designated by the given functions,

     over the given ranges, where a range is described as

     {variable,min,max,(increment)}.  Also accepts options

     like those of ListPlotVectorField3D.

In[133]:=

  PlotVectorField3D[{y,-x,0},{x,-1,1},{y,-1,1},{z,0,2},
  VectorHeads->True];

In[134]:=

  PlotVectorField3D[{Cos[x],Exp[-x] Sin[y],z-y},{x,-1,1},{y,-1,1},{z,-1,1},
  VectorHeads->True];

Up to Vector Fields