| 11. | A cross product in seven dimensions is like the 3-dimensional one.
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| 12. | As is verified using the properties of the vector cross product.
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| 13. | The next step is to eliminate most of the cross products.
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| 14. | :It's definitely not an axiom, just part of the definition of cross product.
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| 15. | Some other Blue Cross products resemble those of other manufacturers.
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| 16. | See Cross product # Cross product as an exterior product.
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| 17. | See Cross product # Cross product as an exterior product.
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| 18. | So it seems the only unexplained arbitrariness is the direction of the cross product.
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| 19. | 3x3 skew symmetric matrices can be used to represent cross products as matrix multiplications.
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| 20. | Torque is an example where the cross product is used.
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