[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 ?

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 $\displaystyle \ell(t)=<t,2t,3t>$ to find the point $\displaystyle X$ solve:

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