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Proving the line lies on the plane

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Does the line with equation (x, y, z) = (5, -4, 6) + u(1,4,-1) lie in the plane with equation (x, y, z) = (3, 0, 2) + s(1,1,-1) + t(2, -1, 1)? Justify your answer algebraically.


    2. Relevant equations


    3. The attempt at a solution
    I started by getting the parametric equation of (x, y, z) = (5, -4, 6) + u(1,4,-1)
    x=5+u
    y=-4+4u
    z=6-u
    I then subbed in u=0 to get a set of points
    x=5
    y=-4
    z=6

    I then got the parametric equation for (x, y, z) = (3, 0, 2) + s(1,1,-1) + t(2, -1, 1)
    x=3+s+2t
    y=0+s-t
    z=2-s+t

    I decided to use the points (5,-4,6)
     
  2. jcsd
  3. Mar 29, 2009 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi soulja101! :smile:
    This is very long-winded :rolleyes:

    you could just put u = 0 in (x, y, z) = (5, -4, 6) + u(1,4,-1), giving (5, -4, 6) immediately :wink:
    why make it so complicated?

    all you have to prove is that (5, -4, 6) minus (3, 0, 2) is a linear combination of (1,1,-1) and (2, -1, 1), and then the same for (1,4,-1) :smile:
     
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