Signed angle between two vectors without a reference plane

Question

(In three dimensions) I\'m looking for a way to compute the signed angle between two vectors, given no information other than those vectors. As answered in this question, it is

Answer 1

Signed angle between two vectors without a reference plane

angle = acos(dotproduct(normalized(a), normalized(b)));

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signed_angle(a, b) == -signed_angle(b, a)

I think that's impossible without some kind of reference vector.