threeDArrowPlot[func_, var1_, var2_, tubesize_List: {.05, .05, .05}, 
   headsize_List: {.05, .05, .05}, plotopts : OptionsPattern[]] := 
  Module[{plot, arrows, lengths},
   plot = 
    Plot3D[func, var1, var2, Boxed -> False, AxesOrigin -> {0, 0, 0}, 
     Evaluate[FilterRules[{plotopts}, Options[Plot3D]]]];
   lengths = 
    DiagonalMatrix[(Charting`get3DPlotRange@plot)[[All, 2]] // 
      Flatten];
   arrows = 
    Table[{RGBColor @@ lengths[[n]], Arrowheads[headsize[[n]]], 
      Arrow[Tube[{{0, 0, 0}, lengths[[n]]}, tubesize[[n]]]]}, {n, 
      3}];
   Show[plot, Graphics3D@arrows]
   ];