Question: Surface normal in vector calculus?

In Vector Calculus there are excellent commands for finding the normal vector to a curve (PrincipalNormal and TNBFrame) but none for finding the surface normal vector. It is possible to display the surface normal vector using PlotPositionVector's normal option, but this is good for visualization only, and the vector can't be used for further calculations.

Am I missing something, or is this really missing form the package?

Two example problems to be solved:
1) We have got the following surface of a cone given by the parametric equation

S1:= PositionVector([u/sqrt(2)*cos(t), u/sqrt(2)*sin(t),u/sqrt(2)])

Get the surface normal vector in the form of a rooted vector.

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2) Another similar problem to be solved is to get the surface normal vector of a plane

P1:= PositionVector([-t, 1+u/sqrt(2), 1+u/sqrt(2)])

Any suggestions? Thanks for your help and coment in advance.

Joe