On Sat, 18 Aug 2001 03:29:21 +0200, Tor Olav Kristensen wrote:
>(Note that I suspect there to be some
>"deeper" relations between the determinant
>of a 3x3 matrix and the cross product of
>two vectors in 3D-space, but I haven't
>studied enough linear algebra to see this
>relation.

Actually, there is.  We were taught that the cross product of two
vectors A and B is the determinant of the matrix given by:

[  x   y   z  ]
[  Ax  Ay  Az ]
[  Bx  By  Bz ]

where x, y, and z are the basis vectors and Ax, Ay, etc. are the components
of the A and B vectors.

Knowing that, it's easy to see the result you've noticed.

-- 
#local R=<7084844682857967,0787982,826975826580>;#macro L(P)concat(#while(P)chr(
mod(P,100)),#local P=P/100;#end"")#end background{rgb 1}text{ttf L(R.x)L(R.y)0,0
translate<-.8,0,-1>}text{ttf L(R.x)L(R.z)0,0translate<-1.6,-.75,-1>}sphere{z/9e3
4/26/2001finish{reflection 1}}//ron.parker@povray.org My opinions, nobody else's

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