Let $\vec { a } = \hat { i } + \hat { j } + 2 \widehat { k } , \vec { b } = 2 \hat { i } - 3 \hat { j } + \widehat { k }$ and $\vec { c } = \hat { i } - \hat { j } + \widehat { k }$ be the three given vectors. Let $\vec { v }$ be a vector in the plane of $\vec { a }$ and $\vec { b }$ whose projection on $\vec { c }$ is $\frac { 2 } { \sqrt { 3 } }$. If $\vec { v } \cdot \hat { j } = 7$, then $\vec { v } \cdot ( \hat { i } + \hat { k } )$ is equal to\\
(1) 6\\
(2) 7\\
(3) 8\\
(4) 9