The vector a = αi + 2j + βk lies in the plane of the vectors b =i + j and c = j + k and bisects the angle between vector b and vector c . Then which one of the following gives possible values of α and β?
(A) α = 2, β = 2
(B) α = 1, β = 2
(C) α = 2, β = 1
(D) α = 1, β = 1