I want to identify if there are conditions where the magnitudes of the dot product AND cross product of two pairs of vectors are equal. So for vectors AOB and XOY, are there combinations of A,B and X,Y which yield (non-trivial) identical dot and cross product magnitudes? I have checked it out "numerically" by enumerating over (x,0) and (x,y) for a range of x,y and theta between the vectors. I get identity and symmetry-related solutions but do not know if I am missing solutions due to sampling limitations etc. Is there a better (analytical) way to find solutions?
2026-03-26 15:16:55.1774538215
Conditions where magnitudes of dot and cross products of vector pairs are equal?
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