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Re: Vectors


In article <6ssuku$m7j at smc.vnet.net>, Olivier Georg
<ogeorg at imtsg12.epfl.ch> wrote:

*  Hi, 
*  
*  I want to do symbolic calculation with vectors, in particular, I want
to *  do a vector product.  But if I declare: *  
*     A = (a b c)
*  
*  and do
*  
*     A x A
*  
*  (which should give zero), but instead I get: *  
*     Cross::"nonn1": "Not all of the arguments are vectors  *     of
required length

You're running into the always bewildering notational inconsistencies of
Mathematica.  Consider

   A = ={{a,b,c}}
   B = {{d},{e},{f}}

(note bracketing).  Are these vectors?  Well, they can be dotted, as in

   A . B

and

   B . A

and you'll get the right answer in each case.  So, if they can be
"dotted", they ought to be "cross-able" as well, right? So try

   Cross[A,B]
   Cross[B,A]
   Cross[A,A]
   Cross[B,B]

and find that _none_ of these work.  Now, page 115 of the Bible says
that Cross[a,b] can also be input as a * b, so try instead

   A * B
   B * A
   A * A
   B * B

and get three or four different answers; some of these work, some don't.

Just don't expect consistency!


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