Point on line between 2 points in distance

• Feb 11th 2013, 03:20 AM
jindave
[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 ?
• Feb 11th 2013, 04:27 AM
Plato
Re: Point on line between 2 points in distance
Quote:

Originally Posted by jindave
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 $\ell(t)=$ to find the point $X$ solve:

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