1. Not finding help here? Sign up for a free 30min 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!

Finding a third plane that has a dihedral angle to two other planes.

  1. Mar 28, 2013 #1
    1. The problem statement, all variables and given/known data

    The acute angle between two planes is called the dihedral angle. Plane x−3y+2z=0 and plane 3x−2y−z+3=0 intersect in a line and form a dihedral angle θ . Find a third plane (in point-normal, i.e. component, form) through the point (-6/7,0,3/7) that has dihedral angle θ/2 with each of the original planes. Do the three planes intersect at a point or in a line? Explain all steps carefully.

    2. Relevant equations

    cosθ=|n1 (dot product) n2| /|n1||n2|,

    3. The attempt at a solution

    I found the dihedral angle of the first two planes to be 1/2, but then I'm not sure what to do after that.
     
  2. jcsd
  3. Mar 28, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Don't you mean you found the cosine of the dihedral angle to be 1/2? Wouldn't your new plane bisect the dihedral angle? Can you get its normal from the given normals?
     
  4. Mar 29, 2013 #3
    Yes, that is what I meant. Do we add the two normals to get the third normal? I am really confused.
     
  5. Mar 29, 2013 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Think about it and draw some pictures. Say you have two vectors with their tails at the same place. Will their sum bisect the angle between them or do you have to have some condition on the vectors to make it happen?
     
  6. Mar 31, 2013 #5
    No because the vectors have to be tip to tail to add up?
     
  7. Apr 1, 2013 #6

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No they don't. Think about the parallelogram rule for addition of vectors. The sum is the diagonal of the parallelogram. What has to be true about the two original vectors for that sum vector to bisect the angle between them?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding a third plane that has a dihedral angle to two other planes.
Loading...