Comments by "zixuan zhao" (@zixuanzhao6043) on "Cross products in the light of linear transformations | Chapter 11, Essence of linear algebra" video.

  1. I have a question about the dual vector we're trying to find here. Couldn't there also be some other projection vector q which is not perpendicular to v-w plane nor its length is the area of the v-w parallelogram but also satisfies that q dot_product (x,y,z) equals the determinant value(the volume) on the right side? Why can't this vector q be the dual vector? Update: I can prove that there could only be only one linear transformation computationally, namely q has to be equal to p from the video. However thinking geometrically I have to do a tiny bit of reasoning. Any ideas?
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