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Homework Help: Finding points on a line in 3d

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data
    It's been a while since ive done this stuff D:

    So Given Points A(a,1,0), B(1,b,0) and C(1,0,c) with |AC|=|BC|=|AB|

    Find the points algebraically

    2. Relevant equations

    Unfortunately, i dont have much knowledge on this. Im sure there's a 3d point slope style formula around somewhere though :s

    3. The attempt at a solution

    At first my guess was to try making it a vector such that SQRT((Xc-Xa)^2+(Yc-Ya)^2+(Zc-Za)^2) and so on, but from there i was confused on how to find the points.

    I appreciate the potential help, thanks guys :D
  2. jcsd
  3. Mar 10, 2010 #2
    Is there a need for X,Y and Z to be in the square? :smile:
  4. Mar 10, 2010 #3


    Staff: Mentor

    Write the vector that represents the vector AB. Write an expression that represents its length. For example, AB = (1 - a, b - 1, 0). |AB| = sqrt((1 - a)^2 + (b - 1)^2).
    Do the same with vector BC. Write an expression that represents its length.
    Do the same with vector AC. Write an expression that represents its length.

    You are given that |AB| = |BC|, |BC| = |AC|, and |AB| = |BC|. Substitute the expressions you already found in these three equations.
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