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Topic: Distance Between Lines in R^3 (fwd)
Replies: 15   Last Post: Sep 13, 2013 1:25 PM

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Tucsondrew@me.com

Posts: 617
Registered: 5/24/13
Re: Distance Between Lines in R^3 (fwd)
Posted: Jul 29, 2013 5:15 PM
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On Thursday, July 25, 2013 8:33:51 PM UTC-7, William Elliot wrote:
> How do we find the shortest distance between two lines L, L' in R^3 ?
>
>
>

Expressing the two lines, L1 and L2, in parametric form where
r,a,b,c,d are vectors, and s,t are scalar parameters,

(L1) r = a + bs,
(L2) r = c + dt,

then the distance between the two lines is given by

g = (a-c)·(b×d) / |b×d|

Found at:

http://2000clicks.com/MathHelp/GeometryPointsAndLines3D.aspx

There nice explanation of why and how this works.





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