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

 Messages: [ Previous | Next ]
 Ken.Pledger@vuw.ac.nz Posts: 1,412 Registered: 12/3/04
Re: Distance Between Lines in R^3 (fwd)
Posted: Jul 28, 2013 5:01 PM

In article <kste74\$gue\$1@news.albasani.net>,
Thomas Nordhaus <thnord2002@yahoo.de> wrote:

> Am 26.07.2013 05:33, schrieb William Elliot:
> > How do we find the shortest distance between two lines L, L' in R^3 ?
> >
> >

>
> How about doing it straight forward from scratch? Let P1(s) = v0 +s*v,
> P2(t) = w0 + t*w be arbitrary points on the line L, L' resp.
> ....

Yes. Then just make the vector (P1(s) - P2(t)) perpendicular to
both lines:

v.((v0 +s*v) - (w0 + t*w)) = 0
w.((v0 +s*v) - (w0 + t*w)) = 0.

Therefore
(v.v)s - (v.w)t = - v.v0 + v.w0
(w.v)s - (w.w)t = - w.v0 + w.w0.

Solve those linear equations for s and t,
then find ||(P1(s) - P2(t))||.

That's all. It's a traditional method in old text-books which aren't
read much any more, and it doesn't need any calculus.

Ken Pledger.

Date Subject Author
7/25/13 William Elliot
7/26/13 quasi
7/26/13 Thomas Nordhaus
7/26/13 Thomas Nordhaus
7/28/13 Ken.Pledger@vuw.ac.nz
7/28/13 Thomas Nordhaus
7/28/13 Virgil
7/28/13 Ken.Pledger@vuw.ac.nz
7/28/13 fom
7/29/13 Thomas Nordhaus
7/29/13 Peter Percival
7/26/13 Bart Goddard
7/27/13 Thomas Nordhaus
7/29/13 Tucsondrew@me.com
9/11/13 Brian Q. Hutchings
9/13/13 Brian Q. Hutchings