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Saturday, 31 October

JEE Main 2024 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 30 January 2024, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

If d1d_1 is the shortest distance between the lines x+1=2y=−12zx+1=2y=-12z, x=y+2=6z−6x=y+2=6z-6 and d2d_2 is the shortest distance between the lines x−12=y+8−7=z−45\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}, x−12=y−21=z−6−3\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}, then the value of 323 d1d2\frac{32\sqrt{3}\,d_1}{d_2} is :

Official answer

16

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Skew Lines
Idea tested
Cartesian Shortest Distance

Same idea in other shifts

Asked 15× in all
  1. 6 Apr 2026, Shift 2 · Q14The shortest distance between the lines x−41=y−32=z−2−3\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3} and x+22=y−64=z−5−5\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5} is :EasySingle correct
  2. 7 Apr 2025, Shift 1 · Q14If the shortest distance between the lines x−12=y−23=z−34\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} and…MediumSingle correct
  3. 8 Apr 2024, Shift 2 · Q16If the shortest distance between the lines x−λ2=y−43=z−34\frac{x-\lambda}{2} = \frac{y-4}{3} = \frac{z-3}{4} and…MediumSingle correct
  4. 9 Apr 2024, Shift 1 · Q16The shortest distance between the lines x−34=y+7−11=z−15\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5} and x−53=y−9−6=z+21\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1} is :EasySingle correct
  5. 1 Feb 2024, Shift 1 · Q16If the shortest distance between the lines x−λ−2=y−21=z−11\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1} and…MediumSingle correct
  6. 27 Jan 2024, Shift 1 · Q18If the shortest distance between the lines x−41=y+12=z−3\dfrac{x-4}{1}=\dfrac{y+1}{2}=\dfrac{z}{-3} and…MediumSingle correct
  7. 31 Jan 2024, Shift 2 · Q17The shortest distance, between lines L1L_1 and L2L_2, where L1:x−12=y+1−3=z+42L_1:\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+4}{2} and L2L_2 is the line,…MediumSingle correct
  8. 10 Apr 2023, Shift 1 · Q15The shortest distance between the lines x+21=y−2=z−52\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2} and x−41=y−12=z+30\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0} isEasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.