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Math Help - point of intersection of two vector

  1. #1
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    point of intersection of two vector

    Hi all,

    I have the lines:

    A: x = 1 + 2t, y = 2+ 3t, z = 3 + 4t

    B: x-2 = (y-4)/2 = (-z -1)/4

    I am having trouble determining the coordinates of the point of intersection of A and B.

    Well i found B in parametric form first:

    x = 2 + t, y = 4 +2t, Z = -4 -4t

    and then i equated each component....

    e.g 1 + 2t = 2 + t; 2 +3t = 4 +2t

    the t values differed for each component and thus i thought there was no point of intersection. However, in the answer there is a point of intersection at (1,2,3). So i am lost here...

    Thanks in advance,
    ArTiCk
    Last edited by ArTiCK; November 15th 2008 at 02:19 PM.
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  2. #2
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    Quote Originally Posted by ArTiCK View Post
    I have the lines:
    A: x = 1 + 2t, y = 2+ 3t, z = 3 + 4t
    B: x-2 = (y-4)/2 = (-z -1)/4
    x = 2 + t, y = 4 +2t, Z = -4 -4t
    Mistake #1. Always use different parameters for different lines.
    So B: x=2+s, y=4+2s, & z=-4-4s.

    Solve for t & s.
    1+2t=2+s
    2+3t=4+2s
    (Be sure to check to see if the solution works for the z value!)
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