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