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Math Help - Calc 3 Help. Finding point of intersection of 2 lines

  1. #1
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    Calc 3 Help. Finding point of intersection of 2 lines

    Hi,
    So the problem states that there are two lines

    L1 : x=12+3t, y=5+3t, z=5+t
    L2 : x=-5+4t, y=-14+5t z=-6+4t

    i've already tried setting the x's, y's, and z's equaling each other.
    i can't seem to find another way to find the point of intersection.
    Any help would be greatly appreciated. thanks you.
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  2. #2
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    Quote Originally Posted by jeugenej1 View Post
    Hi,
    So the problem states that there are two lines

    L1 : x=12+3t, y=5+3t, z=5+t
    L2 : x=-5+4t, y=-14+5t z=-6+4t

    i've already tried setting the x's, y's, and z's equaling each other.
    i can't seem to find another way to find the point of intersection.
    Any help would be greatly appreciated. thanks you.
    The problem is that the same parameter is being used in both equations. They should have ben written:

    L1 : x=12+3t, y=5+3t, z=5+t
    L2 : x=-5+4s, y=-14+5s z=-6+4s

    Now equate:

    12 + 3t = 5 + 4s .... (1)

    5 + 3t = -14 + 5s .... (2)

    5 + t = -6 + 4s .... (3)

    Solve two of these equations simultaneously and check that the solution satisfies the third.
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