Let \( \vec{a} = 2\hat{i} - \hat{j} + 5\hat{k} \) and \( \vec{b} = \alpha \hat{i} + \beta \hat{j} + 2\hat{k} \). If \( \left((\vec{a} \times \vec{b}) \times \hat{i}\right) \cdot \hat{k} = \dfrac{23}{2} \), then \( \left| \vec{b} \times 2\hat{i} \right| \) is equal to:
