Maths - Projections of lines on lines - Forum discussion

By: Nobody/Anonymous - nobody
file Error projecting line onto perpendicular  
2004-09-27 18:36

On this page:
https://www.euclideanspace.com/maths/geometry/elements/line/projections/index.htm

You state that the formula to find the perpendicular component (when projecting one vector against another) is:
A _|_ B = (A x B /|B|) x B /|B|

While I'm too lazy to look at the math, my experimentation shows that this is incorrect. The correct formula should be:

A _|_ B = (-A x B / |B| ) x B / |B|

(When using the original formula, the resulting vector is pointing in the wrong direction, and needs to be swapped to point in the correct direction.)

By: Martin Baker - martinbaker
file RE: Error projecting line onto perpendicular  
2004-09-29 08:52

Thanks very much, I think you are right.

I have corrected the page and added an example at the end to confirm this is correct.

I have not yet checked the matrix and clifford parts.

Martin


metadata block
see also:

 

Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

flag flag flag flag flag flag New Foundations for Classical Mechanics (Fundamental Theories of Physics). This is very good on the geometric interpretation of this algebra. It has lots of insights into the mechanics of solid bodies. I still cant work out if the position, velocity, etc. of solid bodies can be represented by a 3D multivector or if 4 or 5D multivectors are required to represent translation and rotation.

 

Other Math Books

This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2023 Martin John Baker - All rights reserved - privacy policy.