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Jee Main 2025 — Medium JEE math MCQ

Let \( L_1 : \frac{x-1}{2} = \frac{y-1}{3} = \frac{z-1}{4} \) and \( L_2 : \frac{x+1}{2} = \frac{y-2}{3} = \frac{z}{1} \) be two lines. Let \( L_3 \) be a line passing through the point \((\alpha, \beta, \gamma)\) and be perpendicular to both \( L_1 \) and \( L_2 \). If \( L_3 \) intersects \( L_1 \), then \( |5\alpha - 11\beta - 8\gamma| \) equals:
  1. A. \quad 20 \\
  2. B. \quad 18 \\
  3. C. \quad 25 \\
  4. D. \quad 16 \\

Solution

The correct option is **C**. (C. \quad 25 \\)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let L1:x−12=y−13=z−14 L_1 : \frac{x-1}{2} = \frac{y-1}{3} = \frac{z-1}{4} and L2:x+12=y−23=z1 L_2 : \frac{x+1}{2} = \frac{y-2}{3} = \frac{z}{1} be two lines. Let L3 L_3 be a line passing through the point (α,β,γ)(\alpha, \beta, \gamma) and be perpendicular to both L1 L_1 and L2 L_2 . If L3 L_3 intersects L1 L_1 , then ∣5α−11β−8γ∣ |5\alpha - 11\beta - 8\gamma| equals:
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep