## Correction on Projections of lines on planes

2004-05-21
2004-09-02
• It is stated that:
"So the direction is:

(A x B) x B"

It should be:
B x (A x B)
or:
(B x A) x B

(B x A) is indeed out of the page as the text says but (A x B) x B has opposite direction to A || B.

I've also tried to implement the "Alternative using Matrix representation" without success. Since I'm pressed for time, I didn't try to find out why.

• Martin Baker
2004-05-24

Thanks very much for this, Im away from my main computer at the moment but as soon as I get back I will work through this and update the webpage.

Martin

• Martin Baker
2004-06-07

Thanks very much, I have updated the page now. Sorry it took so long but I underestimated all the work waiting for me when I got back to base.

Martin

• Hello,

Some typos :

paragraph : Calculation of the projection on the plane
_   _    _
A || B = |A| xB x A x B  <- unit vectors A,B should be separated ?

paragraph : Calculation of the perpendicular component
Therefore combining these equations gives:

A | B  <- instead of A || B
---

grouping terms,

Alternative using Matrix representation

(A B)x = (Az * Bx* Bz - Bz * Ax* Bz - @ Ax * By* By + Bx * Ay* By) / (Bx2 + By2 + Bz2)
@ missing a minus sign here

Thanks for popularizing so complex stuffs !

Nop

• Martin Baker
2004-09-02