JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(P (-2,-1,1)\) and \(Q \left(\frac{56}{17}, \frac{43}{17}, \frac{111}{17}\right)\) 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 \(.....\)
- A \(150\)
- B \(250\)
- C \(450\)
- D \(350\)
Answer & Solution
Correct Answer
(C) \(450\)
Step-by-step Solution
Detailed explanation
\(RS \equiv(\alpha,-1, \beta)\) \(DR\) of \(PQ \equiv\left(\frac{56}{17}+2, \frac{43}{17}+1, \frac{111}{17}-1\right)\) \(\equiv\left(\frac{90}{17}, \frac{60}{17}, \frac{94}{17}\right)\) \(\frac{90}{17} \alpha+\frac{60}{17}(-1)+\frac{94}{17} \beta=0\) \(90 \alpha+94 \beta=60\)…
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