How would you do the cross product of a two-dimensional vector? I've done three-dimensional ones, but not two-dimensional ones.

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How would you do the cross product of a two-dimensional vector? I've done three-dimensional ones, but not two-dimensional ones.

Mathematics
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The cross product is not defined in R^2.
Then would I just say that there is no cross product?
Sorta -- the cross product is not even applicable :-) ... unless you want a three-dimensional cross product, in which case you mean the vectors have an implicit zero component, e.g. \[u=ai+bj+0k\\ v = ci + dj + 0k\] You can find the three-dimensional cross product, which makes sense -- it's merely the surface normal to the plane defined.\[u \times v = (ad - bc)k\]

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Oh ok. So if I were to have this problem, (the actual problem), let vector a = < 1, 2 > and vector b = < 3, 4 >. FInd the magnitude of vector c if vector c = vector a x vector b. Would it 2?
It is wholly dependent on whether it expects you to do it in R^3 -- if not, then the question is silly because the cross product is not defined for R^2.
Ok...thank you...

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