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 α and β are integers of minimum absolute values, then α²+β² is equal to _ _ _ _ _ _.

Three Dimensional Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jul, Morning shift · Q24

JEE Main 202228 Jul, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let

\mathrm{P}(-2,-1,1)

and

\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

\alpha,-1, \beta

, where both

\alpha

and

\beta

are integers of minimum absolute values, then

\alpha^{2}+\beta^{2}

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.