Re: CrossProduct in Spherical Coordinates

*To*: mathgroup at smc.vnet.net*Subject*: [mg75336] Re: CrossProduct in Spherical Coordinates*From*: roland franzius <roland.franzius at uos.de>*Date*: Wed, 25 Apr 2007 05:42:32 -0400 (EDT)*Organization*: Universitaet Hannover*References*: <f0kbsf$r1k$1@smc.vnet.net>

gogoant06 at yahoo.com.hk wrote: > Dear all, > > I am really new to mathematica and I have met a damn simple problem. > > In[1]:= > <<Calculus`VectorAnalysis` > > In[2]:= > CrossProduct[{1,0,0},{0,1,0},Spherical] > > Out[2]= > {0,0,0} > > Why? Isn't the result supposed to be {0,0,1}, even in spherical > coordinates? Take the cross product of the north polar vector with any pointing towards the equator In: Assuming[r > 0 && R > 0, FullSimplify[CrossProduct[{r, 0, phi}, {R, Pi/2, phi1}, Spherical]]] Out: {r*R, Pi/2, ArcTan[-Sin[phi1], Cos[phi1]]} As you see, the lists in the arguments are the coordinates {r,theta, phi} of the endpoints of the vectors, not their algebraic components in what base so ever (could be cartesian or tangent space base). -- Roland Franzius