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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
     
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