In[]:=
UsingRuledSurfacePlot::usage=" Build the surface that always remains parallel to the XY plane and rests on the curves
2
y
= z, x = 0 and
3
z
= x, y = 0. To use the ResourceFunction, the RuledSurfacePlot[​
c
1
​,​
c
2
​,u] should be considered as follows:

χ
​(u,v) =
c
1
​(u) + v
c
2
​(u)​,
c
1
it's the directrix curve and
c
2
the director curve. The generatrix line passes through the two curves. References: Wolfram MathWorld: ResourceFunction, RuledSurfacePlot. Lehman, Charles H. Geometría Analítica.Ed. Limusa: p.419, 2003; Personal. ";
In[]:=
​​Manipulate[
ζ
1
[u_]:={0,u,
2
u
};
ζ
2
[u_]:={
6
u
,-u,0};
ζ
3
[u_]:={
6
u
,0,
2
u
};Show[ResourceFunction["RuledSurfacePlot"][
ζ
1
[u],
ζ
2
[u],{u,-1,k1},{v,-1,1},PerformanceGoal"Quality",MeshStyleDirective[AbsoluteThickness[0.5],Opacity[0.2]],PlotStyleOpacity[0.1]],Graphics3D[{Red,Ball[
ζ
1
[k1],0.025]}],Graphics3D[{Red,Ball[
ζ
3
[k1],0.025]}],ParametricPlot3D[
ζ
1
[u],{u,-1,1}],ParametricPlot3D[
ζ
3
[u],{u,-1,1}],Graphics3D[{Red,Thick,InfiniteLine[{
ζ
1
[k1],
ζ
3
[k1]}]}],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,PlotRangeAll,ViewPoint{1.3,-2.4,2.},ImageSize700​​],{k1,-1+0.00001,1,0.00001},SaveDefinitionsTrue,ControlPlacementTop,SaveDefinitions->True]
Out[]=
​
k1