An are PQ of a circle subtends a right angle at its centre O . The mid point of the arc PQ is R . If $\overrightarrow{\mathrm{OP}}=\overrightarrow{\mathrm{u}}, \overrightarrow{\mathrm{OR}}=\overrightarrow{\mathrm{v}}$ and $\overrightarrow{\mathrm{OQ}}=\alpha \overrightarrow{\mathrm{u}}+\beta \overrightarrow{\mathrm{v}}$ then $\alpha, \beta^2$ are the roots of the equation