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Re: Re: Re: Wrong behavior of CrossProduct

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  • Subject: [mg8062] Re: [mg8044] Re: [mg7996] Re: [mg7958] Wrong behavior of CrossProduct
  • From: Mark Evans <evans at>
  • Date: Mon, 4 Aug 1997 01:47:45 -0400
  • Organization: None
  • Sender: owner-wri-mathgroup at

> You raise a good point and put your finger on a subtlety that escapes
> most people.  The vector v={0,b,c} in spherical coordinates represents a
> vector of zero length for displacement vectors.  Consider,however, the
> case of a gradient field, such as an electric field.  Certainly we could
> conceive of an electric field that, at some point in space, had no
> radial component, but only a theta or phi component.  The magnitude of
> the field would not be zero because the radial component was zero.  Most
> mechanics and electodynamics textbooks pass over this subtlety because
> physical cross products that occur in nature don't involve displacement
> vectors, they involve field vectors and vector differential operators
> which occur at a local point in space.


Mathematica's vector math is implemented in a package.  Do you think
there should be two packages, one for displacement vectors, another for
field vectors?  What do you think Wolfram Research should do to resolve
these subtleties?  How would you go about resolving them?


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