Example 1

f1=Plot3D[x*Cos[x*y],{x,-2,2},{y,-2,2},AxesLabel->{x,y,z},ViewPoint->{1,1,1}];Show[f1]

Show[f1,ContourPlot3D[y==0,{x,-2,2},{y,-2,2},{z,-2,2}],ParametricPlot3D[{t,0,t},{t,-2,2},PlotStyle->{Red,Thick}]]

Show[f1,ContourPlot3D[x==1,{x,-2,2},{y,-2,2},{z,-2,2}],ParametricPlot3D[{1,t,Cos[t]},{t,-2,2},PlotStyle->{Red,Thick}]]

t1=Plot3D[x,{x,-2,2},{y,-2,2},AxesLabel->{x,y,z},ViewPoint->{1,1,1},PlotStyle->Green];Show[f1,t1]

Example 2

f2=ContourPlot3D[x^2+y^2+z^2==3x*y*z,{x,-3,3},{y,-3,3},{z,-3,3},AxesLabel->{x,y,z},ViewPoint->{1,1,1}];Show[f2]

Show[f2,ContourPlot3D[y==1,{x,-3,3},{y,-3,3},{z,-3,3}]]

t2=Plot3D[-x-y+3,{x,-3,3},{y,-3,3},AxesLabel->{x,y,z},ViewPoint->{1,1,1},PlotStyle->Green];Show[f2,t2]

Example 3

f3=Plot3D[x^2-y^2+2x*y,{x,-2,2},{y,-2,2},AxesLabel->{x,y,z},ViewPoint->{1,1,1}];Show[f3]

Show[f3,ContourPlot3D[y==0,{x,-2,2},{y,-2,2},{z,-5,5}]]

Show[f3,ContourPlot3D[x==0,{x,-2,2},{y,-2,2},{z,-5,5}]]

Manipulate[Show[f3,ContourPlot3D[x==B,{x,-2,2},{y,-2,2},{z,-5,5}]],{B,-2,2}]

Example 4

f4=Plot3D[Sqrt[Exp[Sin[x^3]]]*y*x^2,{x,-3,3},{y,-3,3},AxesLabel->{x,y,z},ViewPoint->{1,1,1}];Show[f4]

Show[f4,ContourPlot3D[y==0,{x,-3,3},{y,-3,3},{z,-10,10}]]

Show[f4,ContourPlot3D[x==1,{x,-3,3},{y,-3,3},{z,-10,10}]]