Let \( \overrightarrow{OP} = \dfrac{\alpha - 1}{\alpha}\, \hat{i} + \hat{j} + \hat{k} \), \( \overrightarrow{OQ} = \hat{i} + \dfrac{\beta - 1}{\beta}\, \hat{j} + \hat{k} \) and \( \overrightarrow{OR} = \hat{i} + \hat{j} + \dfrac{1}{2}\hat{k} \), 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 ______________.
