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

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 ]
quasi

Posts: 10,399
Registered: 7/15/05
Re: Distance Between Lines in R^3 (fwd)
Posted: Jul 26, 2013 1:54 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

William Elliot wrote:

>How do we find the shortest distance between two lines L,L' in R^3?
>
>http://at.yorku.ca/cgi-bin/bbqa?forum=calculus;task=show_msg;msg=0792


Showing a reference is good, but at least give the right link.

The correct link is:

<http://at.yorku.ca/cgi-bin/bbqa?forum=calculus;task=show_msg;msg=0793>

A question of that type can typically be found as a worked example
in a Calculus 3 (Multivariate Calculus) textbook.

One way to do it is as follows ...

Denote the lines as L1,L2.

(1) Let v1,v2 be direction vectors for L1,L2 respectively.

(2) Compute the vector n = v1 x v2 (the cross product).

(3) Take arbitrary points P1,P2 on L1,L2 respectively.

(4) Get an equation for the plane through the point P1 with
normal vector n.

(5) Regarding P1,P2 as vectors, compute the vector difference
w = P2 - P1.

(6) Let p be the vector projection of w onto n.

(7) The distance between the lines L1,L2 is just the norm of p.

quasi



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.