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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?

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  • $\begingroup$ Welcome. Is your question related to Mathematica software? What have you tried? You can search the documentation of Solve and Plot or ParametricPlot. $\endgroup$
    – anderstood
    Nov 2, 2017 at 17:42
  • $\begingroup$ 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 $\endgroup$
    – Angel Hayward
    Nov 2, 2017 at 17:47
  • $\begingroup$ Then I suggest you include your attempts in your question (click on "edit") to get adequate help. $\endgroup$
    – anderstood
    Nov 2, 2017 at 17:53

1 Answer 1

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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}]

enter image description here

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  • $\begingroup$ This is awesome! I ended up doing it a different way, but this will come in handy in the future! Thank you! @egwenesadai $\endgroup$
    – Angel Hayward
    Nov 16, 2017 at 18:36

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