vecPlot[F_,range_]:=GraphicsRow[{
VectorPlot[F,{x,-1.05range,1.05range},{y,-1.05range,1.05range},PlotRange->{{-range,range},{-range,range}},VectorPoints->Fine,ImageSize->500,PlotLabel->"Vektorové pole (OverVector[F])(x,y) = "TraditionalForm[F],FrameLabel->{x,y}],
VectorPlot[(F/(Norm[F])),{x,-1.05range,1.05range},{y,-1.05range,1.05range},PlotRange->{{-range,range},{-range,range}},VectorPoints->Fine,VectorScale->0.02,ImageSize->500,RegionFunction->Function[{x,y,vx,vy,n},(x^2)+(y^2)>0.001range],PlotLabel->"Směr vektorového pole \!\(\*OverscriptBox[\(\(F\)\(\\ \)\), \(⇀\)]\), tj. (OverVector[n])(x,y) = (OverVector[F])(x,y) / |(OverVector[F])(x,y)|, pro (OverVector[F])(x,y) = "TraditionalForm[F],FrameLabel->{x,y}]
}];

vecPlot[{x,y},1]

vecPlot[{y,-x},1]

vecPlot[{x+y,-x+y},1]

vecPlot[{x+y,x-y},1]

vecPlot[{(x^2)-(y^2),2x y},1]