Two adjacent sides of a parallelogram PQRS are given by PQ = j + k and PS = i - j. If the side PS is rotated about the point P by an acute angle α in…

Two adjacent sides of a parallelogram PQRS are given by $\displaystyle \overrightarrow{\mathrm{PQ}}=\hat{j}+\hat{k}$ and $\displaystyle \overrightarrow{\mathrm{PS}}=\hat{i}-\hat{j}$. If the side PS is rotated about the point P by an acute angle $\displaystyle \alpha$ in the plane of the parallelogram so that it becomes perpendicular to the side PQ , then $\displaystyle \sin ^2\left(\frac{5 \alpha}{2}\right)-\sin ^2\left(\frac{\alpha}{2}\right)$ is equal to :