Three particle \( P, Q \) and \( R \) are moving along the vectors \( \vec{A} = \hat{i} + \hat{j} \), \( \vec{B} = \hat{j} + \hat{k} \) and \( \vec{C} = -\hat{i} + \hat{j} \) respectively. They strike on a point and start to move in different directions. Now particle \( P \) is moving normal to the plane which contains vector \( \vec{A} \) and \( \vec{B} \). Similarly particle \( Q \) is moving normal to the plane which contains vector \( \vec{A} \) and \( \vec{C} \). The angle between the direction of motion of \( P \) and \( Q \) is \( \cos^{-1}\!\left( \dfrac{1}{\sqrt{x}} \right) \). Then the value of \( x \) is _______.
