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Homework Help: Distance between lines

  1. Apr 11, 2016 #1
    1. The problem statement, all variables and given/known data

    Okay thanks everyone for taking the time to read this quesiton. Now I sort of know how to do this question but im not entirely sure how I should approach it:

    I have points A(2,1,2) B(3,2,-1) C(-1,2,4) and D(-2,1,3)

    Now a line passes through points A and B and also C and D respectively. What essentially we need to find is that the line that passes through A and B is at least 1 metre apart from the line that passes through C and D
    2. Relevant equations

    Dot Product, cross product. unit vector, shortest distance between two points*

    3. The attempt at a solution

    So in order for there to be a distance we must check if the lines are parallel or not...
    After conducting a test I found that these lines are skewed.

    What I am confused about is this. I have 4 sets of coordinates now I know if I do

    AB = B - A = (1,1,-1)

    and CD = D - C = (-1,-1,-1) I get two vector equations

    Now to find the distance between two vector equations we use vector projection and the unit vector but im not sure how I can lay that out
  2. jcsd
  3. Apr 11, 2016 #2


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    Science Advisor
    Homework Helper
    2017 Award

    So you have two lines ##\vec A + \lambda(\vec B - \vec A)## and ##\vec C + \mu (\vec D - \vec C)##.
    If I follow this example I need the veector product ##\vec N = \vec {AB} \times \vec {CD}## as the main step.

    And note their extremely important tip: make a picture to see what you are doing !
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