Three particles P, Q and R are moving along the vectors → A = ^ i +...

Direction of P, \overset{^}{v}1 = \pm \dfrac{\overset{\to}{A} \times \overset{\to}{B}}{| \overset{\to}{A} \times \overset{\to}{B} |} = \pm \dfrac{\overset{^}{i} - \overset{^}{j} + \overset{^}{k}}{\sqrt{3}}

Direction of Q, \overset{^}{v}2 = \pm \dfrac{\overset{\to}{A} \times \overset{\to}{C}}{| \overset{\to}{A} \times \overset{\to}{C} |} = \pm \dfrac{2\overset{^}{k}}{2} = \pm \overset{^}{k}

Angle between \overset{^}{v}1 and \overset{^}{v}2,

\dfrac{\overset{^}{v}1 \cdot \overset{^}{v}2}{\left|\overset{^}{v}1\right|\left|\overset{^}{v}2\right|} = \dfrac{\pm \dfrac{1}{\sqrt{3}}}{( 1 ) ( 1 )} = \pm \dfrac{1}{\sqrt{3}}

$⇒ x = 3$