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Multivariable Problem need help :P

  1. Sep 17, 2007 #1
    Let L be the line through the point Po(1,2,8) which is parallel to the vector R(3i-j-4k). Find the point at which l intersects the plane through the point p1(-4,0,3) having normal vector n(3i-2j+6k)

    I did the following:
    x=1+3t
    y=2-t
    z=8-4t

    3(x+4)+6(z-3)=0
    3x+6z-6=0

    3(1+3t)+6(8-4t)-6=0
    -15t+45=0
    t=3

    (10, -1, -4)

    Did I do this right?
    Thanks.
     
    Last edited: Sep 17, 2007
  2. jcsd
  3. Sep 18, 2007 #2
    I got a different answer, I'm not quite sure how you're working out the equation of your plane. I ended up with the equation 3x-2y+6z-6=0, which doesn't give quite so nice an answer I'm afraid! Could you explain how your method for working out the equation of the plane works??

    I did it like this:
    equation of a plane is R.n=d
    you are given n and you are given one specific R,
    so equation is R.(3 -2 6) = d

    now you substitute in the specific r to find the d, if that makes sense, so:

    (-4 0 3).(3 -2 6) = -12 +0 +18 = 6

    so you know the equation of the plane is
    R.(3 -2 6) =6

    or, in other words (taking R to be (x y z):
    3x-2y+6z=6
    3x-2y+6z-6=0
     
  4. Sep 18, 2007 #3

    dynamicsolo

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    Homework Helper

    I believe you omitted the y-term in your plane equation.
    Weatherhead's result for the plane looks right to me.
     
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