Re: Re: Vectors

• To: mathgroup at smc.vnet.net
• Subject: [mg13979] Re: [mg13953] Re: Vectors
• From: David Withoff <withoff>
• Date: Sat, 12 Sep 1998 16:59:06 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```> *  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!

Huh?  I don't get it.  Where is the inconsistency?

A={{a,b,c}} and B={{d},{e},{f}} are matrices.  They are not vectors.
A.B and B.A compute matrix dot products.

Cross product is a vector operation.  Cross is not intended for use with
matrices, so Cross[A,B], etc., will not work.

And no, the book does not say you can use a * b for Cross[a, b].  It
says you can use the typeset \[Cross] character (similar to a x b).

This all looks fine to me.  How else could it be designed?

Dave Withoff
Wolfram Research

```

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