Three particles $P , Q$ and $R$ are moving along the vectors $\vec { A } = \hat { \mathrm { i } } + \hat { \mathrm { j } } , \overrightarrow { \mathrm { B } } = \hat { \mathrm { j } } + \widehat { \mathrm { k } }$ and $\vec { C } = - \hat { \mathrm { i } } + \hat { \mathrm { j } }$, 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 $\cos ^ { - 1 } \left( \frac { 1 } { \sqrt { x } } \right)$. Then the value of $x$ is $\_\_\_\_$ .