Physics - Vectors Question with Solution | TestHub

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