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Equations of Lines/Multivariable Calculus

  1. Sep 14, 2013 #1
    1. The problem statement, all variables and given/known data

    Determine whether the lines
    L1:x=t, y=16+4t ,z=8+t
    and
    L2:x=−7+2t, y=−8+6t, z=−3+4t
    intersect, are skew, or are parallel. If they intersect, determine the point of intersection

    2. Relevant equations

    t = -7 + 2s

    16 + 4t = -8 + 6s

    8 + t = -3 + 4s

    3. The attempt at a solution

    I solved the first two equations for s and t then plugged them into the third which confirmed that the lines intersect. To determine the point of intersection, I figured that setting the parametric equations equal to each other and solving for t would give the correct answer, but that doesn't seem to be the right way (I got 7 for the x-coordinate of the intersection).

    So my question is how do I find the intersection?
     
  2. jcsd
  3. Sep 14, 2013 #2
    Once you found out that the lines interesected by solving for t and s, substituting either t in L1 or s in L2 would give you the point of intersection. They should match up if you do both. (And I'm not sure about 7 for the x-coordinate, double check your math).
     
  4. Sep 14, 2013 #3
    Yep, you're right, thanks! It worked.
     
  5. Sep 14, 2013 #4
    Sure thing!
     
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