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MathGroup Archive 2007

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Re: What's wrong?

  • To: mathgroup at
  • Subject: [mg75327] Re: What's wrong?
  • From: jesse.woodroffe at
  • Date: Wed, 25 Apr 2007 05:37:45 -0400 (EDT)
  • References: <f0kbuc$r25$>

>From the documentation on CrossProduct:

"...give the result when the vectors are given in the coordinate
system coordsys"

Mathematica's interpreting the vectors as being defined in a spherical
coordinate system, with each coordinate triplet being read as
{r,theta,phi}, not {x,y,z}. As a result, the second vector in your
cross product has r = 0, i.e. zero length. Hence the (somewhat)
confusing, although correct result.

If you want to actually use spherical vectors in this case, you'd
probably want to use the CoordinatesFromCartesian command. To

  In[]:= cartx = CoordinatesFromCartesian[{1,0,0},Spherical]
Out[]:= {1,Pi/2,0}
  In[]:= carty = CoordinatesFromCartesian[{0,1,0},Spherical]
Out[]:= {1,Pi/2,Pi/2}
  In[]:= sphericalCross = CrossProduct[cartx,carty,Spherical]
Out[]:= {1,0,0}
  In[]:= CoordinatesToCartesian[{1,0,0},Spherical]
Out[]:= {0,0,1}

Owing to the geometrical nature of the operation, I think that it's
safe to say that if you're interested in taking the cross product of
two vectors in an orthonormal basis {e1,e2,e3}, then the result should
be insensitive to the labels you assign to the bases, so long as
you're consistent in your interpretation (handedness &c.).

Jesse Woodroffe

On Apr 24, 2:34 am, "gogoan... at" <gogoan... at>
> In[1]:=
> <<Calculus`VectorAnalysis`
> In[2]:=
> CrossProduct[{1,0,0},{0,1,0},Spherical]
> Out[2]=
> {0,0,0}
> Isn't the result supposed to be {0,0,1}, even in spherical
> coordinates?
> lion

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