Solution to the king's problem with observables that are not mutually complementary

We investigate the king's problem of the measurement of operators n-vector{sub k}{center_dot}{sigma}-vector (k=1, 2, 3) instead of the three Cartesian components {sigma}{sub x},{sigma}{sub y}, and {sigma}{sub z} of the spin operator {sigma}-vector. Here, n-vector{sub k} are three-dimensional real unit vectors. We show the condition over three vectors n-vector{sub k} to ascertain the result for measurement of any one of these operators.