# Orthogonality problem

• Apr 16th 2012, 04:56 AM
drogba
Orthogonality problem
Hi guys,

Hi,

How to have orthogonal values if the value of 3 variables (A,B,C) can only be 1 and -1 ?

So that A.B, B.C and A.C will result in orthogonal (meaning dot product is zero)

So example, A = 1, 1 B = 1 -1 C = -1 1. I am sure whether this is too confusing since not many has replied whether is this possible and if possible any hints / clue to do it?thanks.
• Apr 16th 2012, 09:16 AM
Daniiel
Re: Orthogonality problem
Quote:

Originally Posted by drogba
How to have orthogonal values if the value of 3 variables (A,B,C) can only be 1 and -1 ?

So that A.B, B.C and A.C will result in orthogonal (meaning dot product is zero)

So example, A = 1, 1 B = 1 -1 C = -1 1. I am sure whether this is too confusing since not many has replied whether is this possible and if possible any hints / clue to do it?thanks.

do you mean A = (a, b ,c) B = (q, w, e) C = (z, x, v) where a,b,c,q,w,e,z,x,v= 1 or -1

such that

A.B=A.C=B.C=0 ?

Is this even possible?

I think the closest you can get the dot produce to zero is 1 or -1
• Apr 16th 2012, 11:49 PM
drogba
Re: Orthogonality problem
Yep. So its not possible?strange because i have this kind of question and i am wondering how i can do it. Thanks for the reply anyway. :)
• Apr 17th 2012, 09:59 AM
HallsofIvy
Re: Orthogonality problem
Are the only possible values "1 and -1" or "1, 0, and -1"? The latter seems much more reasonable to me.

Perhaps it would make more sense if you would state the entire problem.
• Apr 18th 2012, 04:30 AM
Mytutoing
Re: Orthogonality problem
The a, b, c are vectors I presume, it is not possible to have three orthoganl vectors in 2D space ie A=(1,1) etc - try and draw it..... full question needed I think to advise on this one