Cartesian coordinate system 3D

The Cartesian space : set of point labelled with coordinate (x, y, z) is an affine space

Two different orientations

3 fingers or thumb or corkscrew rules

Right-handed system Usual in Maths, Physics...
Java system	Left handed system

   / a1     / a2               / a2-a1
 M | b1   P | b2      u = MP = | b2-b1
   \ c1     \ c2               \ c2-c1