Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Tucsondrew@me.com Posts: 1,161 Registered: 5/24/13
Re: Distance Between Lines in R^3 (fwd)
Posted: Jul 29, 2013 5:15 PM

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.

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