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The value of J depends on the mutual orientation of L and S. Here L=1 and S=1.
For J=2, we have J = L + S so L and S are oriented parallel to each other in the same direction.
For J=0, we have J = L – S so L and S are oriented parallel to each other in opposite direction.
For J = 1, the mutual orientation of L and S “halfway between” the other orientations, so L and S are perpendicular to each other.
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