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MathGroup Archive 2002

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Re: cross product

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35383] Re: [mg35367] cross product
  • From: John Browne <jbrowne at swin.edu.au>
  • Date: Wed, 10 Jul 2002 02:20:10 -0400 (EDT)
  • Organization: Swinburne University of Technology
  • References: <200207091050.GAA25676@smc.vnet.net>
  • Reply-to: jbrowne at swin.edu.au
  • Sender: owner-wri-mathgroup at wolfram.com

>
> how can I achieve the CrossProduct of two 4*1 vectors (in homogeneous
> coordinate)?
> For instance: CrossProduct[{a,b,c,1},{d,e,f,1}]
> Thanks in advance
>
> Umby

See the definition of Cross in the Help Browser. The cross product of
two independent vectors in a 3-space is a vector orthogonal to both the
vectors. In 4-space, there is a 2-space of 4-dimensional vectors
(bivector) orthogonal to any two given independent vectors; or else a
vector orthogonal to any three given independent vectors. The
generalization of Cross to a 4-space given in the Help Browser therefore
requires that Cross take three vector arguments in order to generate a
unique vector orthogonal to all three.

Another generalization of Cross to 4-space might take just two vector
arguments and return the bivector orthogonal to both of them.

John



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