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