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Parametric equation of a vector passing through a point and parallel to a line

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Point A (1, -1, 2)

    Line s = 2i - j + t(3i -j +k)


    3. The attempt at a solution

    Ordinarily these are pretty obvious, but in this case the line is also a parametrized vector.

    So if I consider r = r0 + st

    And sub in s as I would do normally, I'd end up getting t^2's, and that's not the correct answer.

    The answer is r = (1, -1, 2) + t(3, -1, 1)

    Which looks like the the t part of the original s line was kept with a new position vector (given point). Why is this?
     
    Last edited: Mar 27, 2012
  2. jcsd
  3. Mar 27, 2012 #2
    You are given a parametric form of the line. It's of the form s = s0 + kt, where now s0 and k are vectors and t is a real number. Two lines are parallel if k1 = k2.
     
  4. Mar 27, 2012 #3
    "Elementary, my dear Watson"

    Thanks for pointing it out!
     
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