The vector \(\vec{a}=α \hat{i}+2\hat{j}+β \hat{k}\) lies in the plane of the vector \(\vec{b}=\hat{i} + \hat{j}\) and \(\vec{c}=\hat{j} + \hat{k}\) and bisects the angle between \(\vec{b}\) and \(\vec{c}\). 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