text: # Equation of a Line of Intersection of Two planes [duplicate]
  
  I have two planes $−11x+20y−23z+25=0$ and $−24x+5y+6z+14=0$. How do I go about finding the equation of the line of intersection? And once I get it, how do i plot both planes and the line?
  
  • Welcome. Is your question related to Mathematica software? What have you tried? You can search the documentation of Solve and Plot or ParametricPlot. Nov 2, 2017 at 17:42
  • I have to find an equation of the line of intersection of the two planes and then plot both the planes and line of intersection in mathematica. I tried using "Solve" but the answer was incorrect (I found the answer manually). @anderstood Nov 2, 2017 at 17:47
  • Then I suggest you include your attempts in your question (click on "edit") to get adequate help. Nov 2, 2017 at 17:53
  
  First get the solution for the line of intersection:
  
  sol = Solve[{-11 x + 20 y - 23 z + 25 ==
  0 && -24 x + 5 y + 6 z + 14 == 0}]
  
  linevec = {x, y, z} /. sol[[1]]
  
  
  then get the z for both planes,
  
  plane1 = z /.
  Solve[-11 x + 20 y - 23 z + 25 == 0, z][[1]]
  plane2 = z /. Solve[-24 x + 5 y + 6 z + 14 == 0, z][[1]]
  
  
  Finally, plot and show them together
  
  g0 = Plot3D[{plane1, plane2}, {x, -3, 3}, {y, -3, 3},
  PlotStyle -> Opacity[.7]];
  g1 = ParametricPlot3D[linevec, {x, -3, 3},
  PlotStyle -> {Red, Thick}];
  Show[{g0, g1}]
  
  
  • This is awesome! I ended up doing it a different way, but this will come in handy in the future! Thank you! @egwenesadai Nov 16, 2017 at 18:36
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