11. A bivector that can be written as the exterior product of two vectors is simple. 12. Each pair is associated with a simple component of the bivector associated with the rotation. 13. So if a general bivector is: 14. This bivector describes the plane perpendicular to what the cross product of the vectors would return. 15. Expansion of the vector bivector product in terms of the standard basis vectors has the following form 16. The quaternion closely corresponds to the exponential of half of the bivector " ?? ". 17. In particular given any bivector "'B "'the rotor associated with it is 18. This can be thought of as the oriented multi-dimensional element " perpendicular " to the bivector . 19. The rotation can be said to take place about that plane, in the plane of the bivector . 20. That is, the components of the quaternion correspond to the scalar and bivector parts of the following expression:
