Maths - Projections of lines on planes - Forum Discussion

By: Nobody/Anonymous - nobody
file Correction on Projections of lines on planes  
2004-05-21 12:56

Here:
https://www.euclideanspace.com/maths/geometry/elements/plane/lineOnPlane/

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.

By: Martin Baker - martinbaker
file RE: Correction on Projections of lines on planes  
2004-05-24 16:18

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

By: Martin Baker - martinbaker
file RE: Correction on Projections of lines on planes  
2004-06-07 14:58

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

By: Nobody/Anonymous - nobody
file RE: Correction on Projections of lines ...  
2004-09-01 14:12

Hello,

Some typos :

paragraph : Calculation of the projection on the plane
But from this page we know that: ...
_ _ _
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

By: Martin Baker - martinbaker
file RE: Correction on Projections of lines on pla  
2004-09-02 14:09

Thanks very much, I have fixed this page as you suggested.

Martin


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