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: Equation of a plane

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the equation of the plane that passes through (5,-5,5) and is perpendicular to the lines of intersection of the planes 3x-2z+1=0 and 4x+3y+7=0

    2. Relevant equations


    3. The attempt at a solution

    I found the cross product of the normals of the planes given. Then used that as the direction vector of the line of intersection. Then I let z=0 and solved for x and y using the equations of the planes given in order to find a point on the line of intersection. The equation for the line of intersection is r=(-1/3,-17/9,0) + s(6,8,9).

    I'm not sure what to do now. Can someone please explain?
  2. jcsd
  3. Mar 28, 2012 #2


    User Avatar
    Science Advisor

    Great! Now use the fact that if <A, B, C> is the normal to the plane and the plane contains the point [itex](x_0, y_0, z_0)[/itex] then the plane is given by [itex]A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0[/itex]. Of course, you use [itex](x_0, y_0, z_0)= (5, -5, 5).

    The "equation of the line of intersection" is irrelevant. The point you are given is not near that line.
  4. Mar 28, 2012 #3
    Ohhh I see! Thanks for the help!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook