I'm not quite sure what angle is desired here.
For a normalized ( length 1 ) vector the components are the "direction cosines", i.e. the cosines of the angles which the vector makes with the positive coordinate axes.
So if the normalized vector is ( something, 0.5, something ) then the angle between the vector and the Y+ axis is ACos( 0.5 ).
For a normalized ( length 1 ) vector the components are the "direction cosines", i.e. the cosines of the angles which the vector makes with the positive coordinate axes.
So if the normalized vector is ( something, 0.5, something ) then the angle between the vector and the Y+ axis is ACos( 0.5 ).