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I'd like to plot a graph of a function using e.g. Plot3D and then a line (in general a curve, in my case a straight line, tangent at some point to the surface just drawn), using e.g. ParametricPlot3D in the same picture. Is it possible? If yes, how?

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Try using Show[] for this. Eg:

Show[
 Plot3D[Sin[x + y^2], {x, -3, 3}, {y, -2, 2}],
 ParametricPlot3D[{Cos[u], Sin[u] + Cos[v], Sin[v]}, {u, 0, 
   2 \[Pi]}, {v, -\[Pi], \[Pi]}]
 ]
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