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Equations of Lines in 3-Space

  1. Mar 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Determine vector, parametric and, if possible, symmetric equations for the line through Q(2, -1, 3) and the mid-point of the line segment from L(3, -2, 5) to M(1, 4, -7).


    2. Relevant equations

    Midpoint equation=( (x1+x2)/2, (y1+y2)/2, (z1+z2)/2)

    3. The attempt at a solution

    Midpoint of LM = (2,1,-1)

    To find the direction vector I'm assuming i must find vector QLM(subscript midpoint)?

    (2,1,-1) - (2,-1,3) = (0,2,-4)

    Vector equation: r= (2,-1,3) + t(0,2,-4)

    Parametric equations:

    x=2, y=-1+2t, z=3-4t

    Symmetric equations:

    x=2; (y+1)/2, (z-3)/-4

    x=2; (y+1)/2, (3-z)/4

    Those are my answers but I'm not sure if my procedure is correct, any help is much appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 30, 2012 #2

    LCKurtz

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    Science Advisor
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    Gold Member

    Your solution looks fine.
     
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