An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If O P = u, O R = v and O Q =α u +β v, then α, β^2…

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