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Intersection of Lines

  1. Jul 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that these lines intersect and what is the intersection point?

    x=1+t
    y=2t
    z=1+3t

    and

    x=3s
    y=2s
    z=2+s


    2. Relevant equations



    3. The attempt at a solution

    I don't know how to start, some help please.
     
  2. jcsd
  3. Jul 26, 2012 #2

    Ray Vickson

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    You want x,y and z on the first line to equal x,y and z on the second line. What does that tell you?

    RGV
     
  4. Jul 26, 2012 #3

    3s= 1 +t
    2s=2t
    2+s=1+3t
     
  5. Jul 26, 2012 #4

    HallsofIvy

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    Good. Normally, you can solve two equations for two unknown numbers while here you have three equations. Solve the first two equations for s and t. Do those values satisfy the third equation? If so, the two lines intersect at the point given by that s and t.
     
  6. Jul 26, 2012 #5
    3s= 1 +t
    2s=2t
    2+s=1+3t

    s = t = 1/2

    how can I show that the lines intersect?
     
  7. Jul 26, 2012 #6

    SammyS

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    Plug the above value for s & t into the following equations for your two lines.

     
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