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