Three ParametricPlot3D in one plot

Questions
1

Hello, how can i do this in the title? i want to see where the three plots are crossing each other.

2

Here is an example:

surface1[u_, v_] := {Sin[u] Cos[v + u], Cos[v] Sin[u], Cos[u - v]}
surface2[u_, v_] := {Sin[u] Cos[v ], Cos[v] + Sin[u], Cos[u - v]}
surface3[u_, v_] := Pi/3 {Sin[u] Cos[v ], Cos[u] Cos[v], Sin[v]}

ParametricPlot3D[{surface1[u, v], surface2[u, v], surface3[u, v]}, {u,
   0 , 2 Pi}, {v, 0, 2 Pi}, BaseStyle -> Opacity[0.5], 
 PlotStyle -> {Red, Blue, Green}, Mesh -> None]
3

i have sth like this
?=1, m=2, ?=0.2, ?= Log[2]/120

ParametricPlot3D[{(?/?*u^m)/(1 + u^m), 
  u, (?/?*u^(m - 1)/(1 + u^m) - ?/?)}, {u, 
  1, 10}, PlotRange -> {{0, 100}, {1, 10}, {0, 5}}]

and i will have two more. How can i do it.i dont have surfaces. It is only the crossing points between two surfaces.

4

There is no guarantee that the three curves will intersect, but you may be able to compute parameters that make them intersect.
In any case, here is an example with curves.

\[Alpha] = 1; m = 2; \[Lambda] = 0.2; \[Mu] = Log[2]/120;
p1 = ParametricPlot3D[{(\[Lambda]/\[Mu]*u^m)/(1 + u^m), 
   u, (\[Lambda]/\[Alpha]*u^(m - 1)/(1 + u^m) - \[Mu]/\[Alpha])}, {u, 
   1, 10}, PlotRange -> {{0, 100}, {1, 10}, {0, .5}}, BoxRatios -> 1, 
  PlotStyle -> {Blue, Thickness[0.01]}]

p2 = ParametricPlot3D[{(\[Lambda]/\[Mu]*u^m)/(1 + u^m), 
   1, (\[Lambda]/\[Alpha]*u^(m - 1)/(1 + u^m) - \[Mu]/\[Alpha])}, {u, 
   1, 10}, BoxRatios -> 1, PlotStyle -> {Red, Thickness[0.01]}, 
  BoxRatios -> 1]

p3 = ParametricPlot3D[{(\[Lambda]/\[Mu]*u^m)/(1 + u), 
   1, (\[Lambda]/\[Alpha]*u^(m - 1)/(1 + u^m) - \[Mu]/\[Alpha])}, {u, 
   1, 10}, BoxRatios -> 1, PlotStyle -> {Green, Thickness[0.01]}, 
  BoxRatios -> 1]

Show[p1, p2, p3]
5

Yes, i know. I have to change the parameters in order to find 3 fixed points.

6

Thank you very much. I will test it in a little bit.