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Distance between lines

  1. Aug 3, 2011 #1
    1. The problem statement, all variables and given/known data

    In R3, consider the line l given by the equations {x=t,y=t,z=t} and the line m given by the equations {x=s,y=2s-1,z=1}. Let P be a point on l, and let Q be a point on m. Find the values of t and s that minimize the distance between the lines by minimizing the squared distance abs(P-Q).

    2. Relevant equations

    [P] = A(ATA)-1AT

    3. The attempt at a solution

    Let the basis for l be span{(1, 1, 1)} and the basis for m be span{(1,2,0),(0,-1,1)}

    From here on I actually don't know what to do:( Do I have to apply the formula to both lines?

    Please help!
     
  2. jcsd
  3. Aug 3, 2011 #2

    tiny-tim

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    hi derryck1234! :smile:

    what's the difficulty? :confused:

    P is (t,t,t) and Q is (s,2s-1,1), so minimise PQ2 (as the question says :wink:)
     
  4. Aug 3, 2011 #3
    Ok. But are you saying that I should use calculus to do that? Because in my textbook, whenever we need to use calculus, the question has a line before it saying: FOR THOSE READERS WHO HAVE STUDIED CALCULUS...

    This one doesn't?

    To be honest, I don't even think I remember how to do it...would it entail working out abs(P-Q), then finding the derivative and then setting it to zero?

    Thanks

    Derryck
     
  5. Aug 3, 2011 #4

    tiny-tim

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    Last edited by a moderator: Apr 26, 2017
  6. Aug 4, 2011 #5
    Thanks tiny tim. I do hope my correspondence maths course goes ok. It is not easy let me tell you...doin maths via correspondence:( Especially in South Africa!
     
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