Vector Algebra

Three particles P, Q and R are moving along the vectors \(\overrightarrow A = \widehat i + \widehat j\), \(\overrightarrow B = \widehat j + \widehat k\) and \(\overrightarrow C = - \widehat i + \widehat j\) 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 \(\overrightarrow A\) and \(\overrightarrow B\). Similarly particle Q is moving normal to the plane which contains vector \(\overrightarrow A\) and \(\overrightarrow C\). The angle between the direction of motion of P and Q is \({\cos ^{ - 1}}\left( {{1 \over {\sqrt x }}} \right)\). Then the value of x is _______________.