Cross Product

a.k.a. the vector product

                  / x1   / x2     / y1.z2 - y2.z1
 u x v = u ^ v =  | y1 x | y2  =  | x2.z1 - x1.z2
                  \ z1   \ z2     \ x1.y2 - x2.y1

u x v is a vector perpendicular to both u and v , which direction is given by the usual right handed rule, and the length, by :

|| u x v || = || u || . || v || . sin (uˆv)

now we are able to get the angle ...

Before going further, let's check those properties (again ?)

u x v is normal to the plane defined by u and v (and a chosen point)

if ( i, j, k ) are the set of vectors that define your right handed three-dimensional coordinate system, then k = i x j

                  / 1   / 0     / 0.0 - 1.0     / 0
 i x j = i ^ j =  | 0 x | 1  =  | 0.0 - 1.0  =  | 0  =  k
                  \ 0   \ 0     \ 1.1 - 0.0     \ 1

All the usual right handed rules could be applied, the 3 fingers, the thumb and the others, the screwdriver and the corkscrew for the French ...

Other simple problem : How to compute the normal to a plane ?

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