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p = Plot3D[x^2 + y^2, {x, -1, 1}, {y, -1, 1}]; pv = VectorPlot3D[{{2 x, 2 y, 0}, {-2 y, 2 x, 0}}, {x, -1, 1}, {y, -1, 1}, {z, -0.01, 0.01}, PlotRange -> {Automatic, Automatic, {-1, 1}}]; Show[pv, p]



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