The Sub Nil Space

The sub Nil plane 
The first function allows the users to manipulate the {x,y,z} to see what plane in nil space they can travel on. In this example, the spanning vectors for the plane are {1,0, 2y} and {0, 1, -2x}.
The users can change {x,y,z} using the sliders, The users should not change any of the code

Evaulate this cell

Clear[x,y]
Manipulate[u={1,0,2 g};
v={0,1,-2 f};
e=Cross[u,v];
{a,b,c}=e;
d=e.{f,g,h};
Plot3D[Tooltip[(-a/c)*x+(-b/c)*y+d/c],{x,-50,50},{y,-50,50},PlotRange->{-200,200},PlotLabel-> {f,g,h},Mesh->{{{f, Thick}},{{g, Thick}}},ClippingStyle->None], {{f,0,"initial x"},-50,50},{{g,0,"initial y"},-50,50},{{h,0,"initial z"},-50,50}]