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[Phys-L] Re: Area vector



While none of the answers are blatantly wrong, the hisory is
interesting and is recounted in Morris Kline's book on <Mathematical
Thought>. It started with Hamilton's attempt to generalize complex
numbers to 3 dimensions - he accordingly invented quaternions - and ended
with Gibbs' formulation of 3-d vector algebra. Grassman, in the meantime,
found a different, but equivalent, formulation which is readily
applicable to more than 3 dimensions. The Gibbs formulation, using the
unit vectors i,j,k. requires iXj =k, which is the answer to Tony's
question, since the magnitude of an arbitrary cross-product is the area of
the parallelogram defined by the two vectors in the cross-product.
Amusingly, the Gibbs cross-product is already implied by the
algebra of Hamilton's quaternions.
Regards,
Jack





On Tue, 29 Mar 2005, Tony Wayne wrote:

Does any one know why the "area vector" for a surface is defined as
being normal to the plane of the surface instead of parallel to the
plane of the surface?
-Tony
= = = = = = = = = = = = = = = = = = = = =
Tony Wayne
twayne@albemarle.org
http://physics.k12albemarle.org



--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley
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