Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Ken.Pledger@vuw.ac.nz

Posts: 1,368
Registered: 12/3/04
Re: Distance Between Lines in R^3 (fwd)
Posted: Jul 28, 2013 5:01 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 ?
> >
> > 2. http://at.yorku.ca/cgi-bin/bbqa?forum=calculus;task=show_msg;msg=0792
> >

>
> 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.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.