Let $\overrightarrow{OP} = \frac{\alpha-1}{\alpha} \hat{i} + \hat{j} + \hat{k}$,$\overrightarrow{OQ} = \hat{i} + \frac{\beta-1}{\beta} \hat{j} + \hat{k}$ and $\overrightarrow{OR} = \hat{i} + \hat{j} + \frac{1}{2} \hat{k}$ be three vectors,where $\alpha, \beta \in \mathbb{R} - \{0\}$ and $O$ denotes the origin. If $(\overrightarrow{OP} \times \overrightarrow{OQ}) \cdot \overrightarrow{OR} = 0$ and the point $(\alpha, \beta, 2)$ lies on the plane $3x + 3y - z + l = 0$,then the value of $l$ is:
- A$5$
- B$4$
- C$6$
- D$7$
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