MyGoalPrep LogoMyGoalPrep.com

Jee Main 2025 — Medium JEE math MCQ

Let $L_1 : \frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ and $L_2 : \frac{x-3}{2} = \frac{y-4}{3} = \frac{z-5}{4}$ be two lines. Then which of the following points lies on the line of the shortest distance between $L_1$ and $L_2$?
  1. A. $\left( \frac{14}{5}, -3, \frac{22}{3} \right)$
  2. B. $\left( -\frac{5}{3}, -7, 1 \right)$
  3. C. $\left( 2, 3, \frac{1}{2} \right)$
  4. D. $\left( \frac{5}{3}, -1, \frac{1}{2} \right)$

Solution

The correct option is **A**. (A. $\left( \frac{14}{5}, -3, \frac{22}{3} \right)$)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let L1:x−12=y−23=z−34L_1 : \frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} and L2:x−32=y−43=z−54L_2 : \frac{x-3}{2} = \frac{y-4}{3} = \frac{z-5}{4} be two lines. Then which of the following points lies on the line of the shortest distance between L1L_1 and L2L_2?
AI hints
Ask for a nudge. Keep it specific.