1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find the angle between two planes

  1. Mar 9, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the angle between the plane 3x+5y+7z = 1 and the plane z = 0.

    2. Relevant equations

    3. The attempt at a solution
    Hi, I know that I need to have both these planes in the form (x,y,z) and then find the dot product to find the angle between them. The problem I am having is with putting them in that form, at first I assumed plane 1 would just be (3,5,7) and plane 2 would be (0,0,1), but I have also read that to find the angle between to planes I need the normal vector to each plane, and this has confused me. Using these vectors I came up with the answer 30.8°, but I don't know if what I did was right! Any help would be appreciated!
  2. jcsd
  3. Mar 9, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    (3,5,7) IS the normal vector to the plane, not the plane itself. Same for (0,0,1). It sounds like you are doing it correctly. I don't get the answer you got though. Can you show how your numbers worked?
  4. Mar 9, 2013 #3
    I think the answer should be 39.8
  5. Mar 9, 2013 #4
    can anyone help me with this question:
    Find the angle between
    (a) the line L1 given by the equations y = 2z, x = 0, and
    (b) the line L2 given by the equations x = 3z, y = 0.
  6. Mar 10, 2013 #5
    Sorry, working it out again I got 39.79;
    a.b=(3x0+5x0+7x1) = 7
    ∴θ=cos-1(a.b/|a||b|)= 39.79

    So for any equation ax+by+cz=d, will the normal vector always be (a,b,c)?
    Thanks for your replies:)
  7. Mar 10, 2013 #6


    User Avatar
    Science Advisor

    AXidenT posted this same question at
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted