A vector $\vec { a } = \alpha \hat { i } + 2 \hat { j } + \beta \hat { k }$ $(\alpha, \beta \in R)$ lies in the plane of the vectors, $\vec { b } = \hat { i } + \hat { j }$ and $\vec { c } = \hat { i } - \hat { j } + 4 \hat { k }$. If $\vec { a }$ bisects the angle between $\vec { b }$ and $\vec { c }$, then\\
(1) $\vec { a } \cdot \hat { i } + 3 = 0$\\
(2) $\vec { a } \cdot \hat { i } + 1 = 0$\\
(3) $\vec { a } \cdot \widehat { k } + 2 = 0$\\
(4) $\vec { a } \cdot \widehat { k } + 4 = 0$