The vector $\overrightarrow{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}$ lies in the plane of the vectors $\overrightarrow{b}=\hat{i}+\hat{j}\; and \overrightarrow{c}=\hat{j}+\hat{k}$ and bisects the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$.Then which one of the following gives possible values of $\alpha$ and $\beta$ ?

Question

( A ) $\alpha=1$$\beta=2$
( B ) $\alpha=2$$\beta=2$
( C ) $\alpha=2$$\beta=1$
( D ) $\alpha=1$$\beta=1$