If \( \vec{P} = 3\hat{i} + \sqrt{3}\hat{j} + 2\hat{k} \) and \( \vec{Q} = 4\hat{i} + \sqrt{3}\hat{j} + 2.5\hat{k} \) then, The unit vector in the direction of \( \vec{P} \times \vec{Q} \) is \( \frac{1}{x}\left( \sqrt{3}\hat{i} + \hat{j} - 2\sqrt{3}\hat{k} \right) \). The value of \( x \) is:
