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Math Bundle 3 - Cross Product Sign Issue #66
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In my opinion, "negative" and "positive" should be replaced in the following results. It would be nice if someone else also supports my opinion.
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ykaya932 commentedon Apr 10, 2021
Or of course, it would also be great if someone else points out my mistake
orbitstabilizer commentedon Dec 3, 2022
Interpretation of signs depends on what one means by "u lies on the right/left hand side of v", since being on the right/left of something is not an absolute concept. If you orient yourself facing +z direction then the given signs make sense. And, I think, this was what the author had in mind when writing this. Figure 8, in the previous section where the cross product is introduced, shows intended orientation. So, I think, we should make the implicit orientation explicit, and/or, maybe, also change the signs so the orientation would be more "natural".
P.S. for me facing -z direction is more "natural", which would result in your signs. I think, this is the orientation one would normally think imagining x-y plane.