Let $\overrightarrow { O P } = \frac { \alpha - 1 } { \alpha } \hat { i } + \hat { j } + \hat { k } , \overrightarrow { O Q } = \hat { i } + \frac { \beta - 1 } { \beta } \hat { j } + \hat { k }$ and $\overrightarrow { O R } = \hat { i } + \hat { j } + \frac { 1 } { 2 } \hat { k }$ be three vectors, where $\alpha , \beta \in \mathbb { R } - \{ 0 \}$ and $O$ denotes the origin. If $( \overrightarrow { O P } \times \overrightarrow { O Q } ) \cdot \overrightarrow { O R } = 0$ and the point $( \alpha , \beta , 2 )$ lies on the plane $3 x + 3 y - z + l = 0$, then the value of $l$ is $\_\_\_\_$ .