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What about the cross product for 7 dimensions? I'm assuming we won't necessarily be using it, I just don't really know much about it other than that it exists.


What are some use cases in which we would want to use a negative area/how can area be negative?


If we wanted something that worked similarly in 4D, would we have an operator that takes three vectors and returns a fourth?


Why does the direction matter here? If we only want to use the cross product to get a vector orthogonal to both vectors, both direction should work. Is there any practical reason that forces us to figure out its direction?


Didn't really get it for 2d. Why we will use it in 2D?


Does cross product have any meaning in higher dimensional space?


I think some software or system tend to use left-handed coordinate systems, I wonder which is more general for CG and why the aother would be used in nother scenarios?


Suppose u and v have both coordinates in meters, for example. It just occurred to me that the cross product would have all of its coordinates have units of square meters. This somehow suggests that the cross product (from a more physics / physical interpretation) doesn't really represent a vector of the same "kind" as the two input vectors. Is there something more to be said about this observation?