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Math Help - Parametric Equation for a Line

  1. #1
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    Parametric Equation for a Line

    Find parametric equations for the line through the point, that is parallel to the given plane, and perpendicular to the following line.

    Given information:
    (0,1,2)
    x + y + z = 4
    x = 1 + t, y = 1 - t, z = 2t
    x = 3s

    Need to find:
    y = ?
    z = ?

    Attempt:
    x = 3s = 1 + t
    t = 3s - 1

    y = 1 (3s -1) = 2 - 3s
    z = 2 (3s -1) = 6s -1

    Not sure where I went wrong, or if I even did this correctly. Thanks in advance for any help or suggestions.
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  2. #2
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    The direction vector of the line is <1,1,1>\times<1,-1,2>.
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