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Understanding the cross product with geometric algebra: a. Prove that the unit pseudoscalar in G3, I = ezezez = e.1e21e3
Posted: Fri Mar 04, 2022 10:17 am
by answerhappygod
- Understanding The Cross Product With Geometric Algebra A Prove That The Unit Pseudoscalar In G3 I Ezezez E 1e21e3 1 (37.14 KiB) Viewed 74 times
Understanding the cross product with geometric algebra: a. Prove that the unit pseudoscalar in G3, I = ezezez = e.1e21e3, commutes with everything in G3. Is the same true in Gz? b. Show that, given any bivector B in G3, there is a unique vector v such that B = v I. We say that "v is dual to B". c. Show that we can define u x VEU AVI'', where u x v is the usual cross product (which only makes sense in 3D). (Note that we define the cross product in terms of the wedge product, and not the other way around, because the wedge product is more general.) Thus in 3D only we have the nice relation uv = u.v + uxvI.