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## Main Question or Discussion Point

One can represent the mean of the angular momentum operator as a vector. But

**what is the (mathematical) justification**to represent the operator by a vector which has a direction that the operator has not. Yet worse, l(l+1) h2 is the proper value of operator**L^2**and from**such result**it is assumed that (l(l+1))^1/2 is the length of operator**L**. Such trick-representation seems to be a strong convention, but it does not make it mathematically correct.