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Linear Algebra orthogonality problem

  1. Apr 11, 2014 #1
    1. The problem statement, all variables and given/known data
    Let W be the intersection of the two planes

    x + y + z = 0 and x - y + z = 0

    In R3. Find an equation for Wτ


    2. Relevant equations



    3. The attempt at a solution

    So, W = {(x, y, z) l 2y =0}

    I don't think that is a correct was to represent W being the intersection of the planes though.

    I can find Wτ after I know how to find my equation for W.

    Any thoughts for how to find the equation for W?
     
  2. jcsd
  3. Apr 11, 2014 #2

    LCKurtz

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    ##y=0## alright, but you need more. You also need ##x=-z## for ##(x,y,z)## to be on both planes. Do you see how to write the equation from that?
     
  4. Apr 11, 2014 #3
    Im not seeing how to get x = -z......
     
  5. Apr 11, 2014 #4

    LCKurtz

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    Look at the equations of the two planes when ##y=0##.
     
  6. Apr 11, 2014 #5
    Ok so you "Let" x = -z, so that way when y=0 the equation for the two planes become x + z = 0

    so x has to be equal to - z to make -z + z = 0 right?
     
  7. Apr 11, 2014 #6

    LCKurtz

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    Yes. So what is the equation of the line of intersection?
     
  8. Apr 11, 2014 #7
    x+z = 0?
     
  9. Apr 11, 2014 #8

    LCKurtz

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  10. Apr 11, 2014 #9
    A tip is to see x=-z as (x-0)/1 = (z-0)/-1.
     
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