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Point of intersection of two lines

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the point of intersection of two lines
    x = -9 + 5t
    y = 1 + t
    z = 10 - 4t

    and

    x = -2 -3t
    y = 5 + 2t
    z = 5 + 3t


    2. Relevant equations
    N/A


    3. The attempt at a solution
    I have read that you should set two of the equations equal to find the value of t, and that value of t should hold for the third equation, but whenever I do that I get two different values for t, and neither of them hold up in the third equation. What am I doing wrong?
     
  2. jcsd
  3. Mar 9, 2010 #2

    tiny-tim

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    Hi dcramps! :smile:

    Where the two lines intersect, the parameter t will be different on each line. :wink:

    So call the parameter for the second line u, then set two of the equations equal to find the values of t and u. :smile:
     
  4. Mar 9, 2010 #3
    Thanks! Now I have my t and u values, and plugging them into the third equation gives me equality...but where do I go from here? Do I plug them into all of the original equations and use the results as my intersection point?
     
  5. Mar 9, 2010 #4

    tiny-tim

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  6. Mar 9, 2010 #5
    Excellent. Thanks for your help :)
     
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