cross-product in cylindrical problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg51258] cross-product in cylindrical problem*From*: "news" <anonym at bamboo.com>*Date*: Sun, 10 Oct 2004 05:52:32 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I'm really puzzled by this behavior of Mathematica, I have two vectors in cylindrical coordinates and would like to take their cross-product in cylindrical, but it seems to give me incorrect answer, see below: define parametric path {r,phi,z} In[110]:= f[\[Rho]_, \[Phi]_] = {\[Rho], \[Phi], 0} Out[110]= {\[Rho], \[Phi], 0} take derivates of path w.r.t. r then w.r.t phi, get {1,0,0}, and {0,1,0} In[113]:= v1 = D[f[\[Rho], \[Phi]], \[Rho]] v2 = D[f[\[Rho], \[Phi]], \[Phi]] Out[113]= {1, 0, 0} Out[114]= {0, 1, 0} then cross them in cylindrical coords, and should get {0,0,1}, but instead get wrong answer below In[117]:= n = CrossProduct[v1, v2, Cylindrical[\[Rho], \[Phi], z]] // FullSimplify Out[117]= {0, 0, 0} As you can see, when I cross {1,0,0} with {0,1,0} in cylindrical coords, I get {0,0,0}, when I should be getting {0,0,1}. Can anyone help?

**Follow-Ups**:**Re: cross-product in cylindrical problem***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>