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

**References**:**cross product***From:*"Umby" <umprisco@unina.it>