@FlatterMann Yeah i misread question lol. comment deleted :P

OK so the magnitude of the cross product IS the area of a parallelogram constructed from its vectors. That satisfies my first question. I get that these are separate operations, but is there an example of using the cross product that is motivated by this connection tho?

Interesting... What do you mean that a warp geometry could be constructed without any energy at all? My understanding was that mass (and therefore energy?) is responsible for the warping of spacetime.

@Ghoster, maybe a better question is when would you want to do this. I will update question for clarification

@A.V.S. I'm not sure. I don't have a lot of experience with general relativity, nor with warp drives. But my point in asking this question is to understand how feasibility of warp drives changes when you deal with super-luminal vs sub-luminal travel. You are right that this is very 'sci-fi-ey" in its language, maybe thats due to my limited education.

@A.V.S. A sub-luminal warp drive would just be a solution to the Einstein Field Equations, (similar to the Alcubierre Metric) where the warping of space allows for the 'riding' of a warped spacetime. But where v<c. This is a 'Class 1" warp drive in the paper I linked above. Clearly warp drives are not necessary for subluminal travel, but I don't see how that's relevant to my question.

@mmesser314 I'll admit I'm not exactly a physicist but this area has always interested me. However, my understanding of Alexey Bobrey's recent paper showed that negative mass/energies are not necessary. arxiv.org/abs/2102.06824