JEE Main 2026 — 4 April, Morning Shift — Question 37

$\mathrm{P}(2 \lambda, 3 \lambda, 3 \lambda-1)$ and $\mathrm{Q}(-\mu-1, \mu+2,4 \mu)$ D.R of PQ $2 \lambda+\mu+1,3 \lambda-\mu-2,3 \lambda-4 \mu-1$, $\frac{2 \lambda+\mu+1}{1}=\frac{3 \lambda-\mu-2}{-1}=\frac{3 \lambda-4 \mu-1}{2}$ Solving $\lambda=\frac{1}{5}$ and $\mu=\frac{-8}{15}$ $\mathrm{P}\left(\frac{2}{5}, \frac{3}{5}, \frac{-2}{5}\right) \& \mathrm{Q}\left(\frac{-7}{15}, \frac{22}{15}, \frac{-32}{15}\right)$ $\mathrm{PQ}^{2}=\left(\frac{13}{15}\right)^{2}+\left(\frac{13}{15}\right)^{2}+\left(\frac{26}{15}\right)^{2}$ $\alpha^{2}=\frac{1014}{225}$

$\therefore 225 \alpha^{2}=1014$