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!

Homework Help: Finding the standard equation for a plane orthogonal to two other planes

  1. Oct 2, 2011 #1
    1. The problem statement, all variables and given/known data
    let p1 and p2 be planes in R3, with respective equations:

    x+5y-z=20 and 2x+5y+2z=20

    These planes are not parallel. Find the standard equation for the plane that is orthogonal to both of these planes and contains the origin.

    3. The attempt at a solution

    I have only managed to garner a few facts from the problem, however I don't know how to use them. Here they are:

    Since the plane, we'll call it ζ that we are looking for is orthogonal to both of these planes, ζ must contain the normal vectors of both of these planes. These normal vectors, for p1 and p2 respectively, are (1,5,-1) and (2,5,2). Also, the standard equation of ζ must be equal to 0, as ζ contains the origin, ie:

    ax+by+cz=0, since the origin is (x,y,z)=(0,0,0)

    That's as far as I got. The information is there, I just have no clue how to use it.
  2. jcsd
  3. Oct 2, 2011 #2
    Well, you've said that your plane must contain the normal vectors (x,y,z) = (1,5,-1) and (2,5,2) and looks like ax+by+cz = 0. Maybe you could put those vectors into the formula for the plane and come up with some equations...
  4. Oct 2, 2011 #3
    Oh wow. Thanks a bunch, can't believe I didn't see that XD
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook