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Math Help - Point on line between 2 points in distance

  1. #1
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    [Solved] Point on line between 2 points in distance

    How I can find the Point, if have know this:
    Point A[0,0,0] - origin
    Point B[1,2,3]
    Distance D = 5


    And i want find the Point X, which is on the Line between points A and B in distance D.

    So know this:
    (x1 - a1/b1 - a1) = (x2 - a2/b2 - a2) = (x3 - a3/b3 - a3) = λ

    and

    sqrt((x1 -a1)2 +(x2 -a2)2 +(x3 -a2)2) = D

    =>

    sqrt((x1)2 +(x2)2 +(x3)2) = D

    How i can find point X ?
    Last edited by jindave; February 11th 2013 at 05:07 AM. Reason: Solved
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  2. #2
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    Re: Point on line between 2 points in distance

    Quote Originally Posted by jindave View Post
    How I can find the Point, if have know this:
    Point A[0,0,0] - origin
    Point B[1,2,3]
    Distance D = 5
    And i want find the Point X, which is on the Line between points A and B in distance D.

    The line is \ell(t)=<t,2t,3t> to find the point X solve:

    \sqrt{t^2+(2t)^2+(3t)^2}=5.
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