Timeline for Cross products/avoiding using your hand for the right hand rule in E and M
Current License: CC BY-SA 4.0
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| May 16, 2019 at 17:52 | comment | added | Derek Elkins left SE | Specifically, if you wanted the cross product (for 3D GA) for some bizarre reason, you'd have a formula like $u\times v = (u\wedge v)I^{-1}$ where $I$ is the unit pseudoscalar, except that there're two unit pseudoscalars, $\vec x\wedge\vec y\wedge\vec z$ and $\vec x\wedge\vec z\wedge\vec y$. This is where the handedness of the cross product comes in. $\vec x\times\vec y=\pm\vec z$ becomes revealed as $\vec x\wedge\vec y=I\vec z$ which, by having the pseudoscalar explicit, is independent of handedness. What is dependent is whether $I\vec z$ is positive $\vec x\wedge\vec y$ or negative. | |
| May 16, 2019 at 1:29 | history | answered | Mike | CC BY-SA 4.0 |