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Math Help - Coplanar Symmetric Equations Problem

  1. #1
    Junior Member Morphayne's Avatar
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    Exclamation Coplanar Symmetric Equations Problem

    Problem:

    Show that the lines L1: \frac {x-2}{3} = \frac {y-3}{5} = \frac {z-1}{1} and L2: \frac {x-4}{1} = \frac {y-1}{7} = \frac {z}{2} are coplanar.

    Comments:

    This is part of my final exam prep. Please help me out.
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  2. #2
    MHF Contributor

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    Note that the point (5,8,2) is on both lines.
    Two intersecting lines determine a plane.
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  3. #3
    Junior Member Morphayne's Avatar
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    Quote Originally Posted by Plato View Post
    Note that the point (5,8,2) is on both lines.
    Two intersecting lines determine a plane.
    How did you get that coordinate?
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  4. #4
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    Quote Originally Posted by Morphayne View Post
    How did you get that coordinate?
    Actually, I just looked at it and saw it.
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  5. #5
    Junior Member Morphayne's Avatar
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    Quote Originally Posted by Plato View Post
    Actually, I just looked at it and saw it.
    Well where do you see it?
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  6. #6
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    Quote Originally Posted by Morphayne View Post
    Well where do you see it?
    Are you saying that you do not see that (5,8,2) is on both lines? Surely not!
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  7. #7
    Junior Member Morphayne's Avatar
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    Forget it... I figured it out by finding the parametric equations for each of the lines and substituted t=1.
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