Let P (-2,-1,1) and Q (56/17, 43/17, 111/17) be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are α,-1, β, where both…

Let $\displaystyle \mathrm{P}(-2,-1,1)$ and $\displaystyle \mathrm{Q}\left(\frac{56}{17}, \frac{43}{17}, \frac{111}{17}\right)$ be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are $\displaystyle \alpha,-1, \beta$, where both $\displaystyle \alpha$ and $\displaystyle \beta$ are integers of minimum absolute values, then $\displaystyle \alpha^2+\beta^2$ is equal to \_\_\_\_.