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I need to plot a vector field 2x,2y,0 which is the gradient of the function x^2+y^2. I need to plot it only in some interesting points (points on the paraboloid x^2+y^2). So I tried something like

a=Table[{{x,y,x^2+y^2},{2x,2y,0}},{x,-2,2,0.5},{y,-2,2,0.5}]

ListVectorPlot3D[a]

It did not work. The definition of ListVectorPlot3D[{{x,y,z},{a,b,c}},...] says that it generates a 3D vector plot from vector field values {a,b,c} given at specified points {x,y,z}.

Any idea how I might plot that gradient on the paraboloid ? It would be really unpleasant if I had to do every single vector with Graphics3D[]

thanks

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# Mathematica, gradient plot on the graph

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