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It has never been formally told me, but I noticed angular momentum is taken as two seperate magnitudes and not three. i.e. in quantum mechanics there's an operator for [itex]\bf{L}^2[/itex] and for [itex]L_z[/itex] and this should be enough.

My question is whether knowing a vector's magnitude (it's "absolute value") and one of it's components is sufficient to determine the other

**two**components (i.e. [itex]L_x[/itex] and [itex]L_y[/itex])

I guess that for a

**general vector**this would be a NO. but specifically angular momentum is a cross product... and I think it matters.

Thanks in advance.