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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 25 July 2022, Shift 2, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

The shortest distance between the lines x+7−6=y−67=z\frac{x+7}{-6}=\frac{y-6}{7}=z and 7−x2=y−2=z−6\frac{7-x}{2}=y-2=z-6 is
  1. (1)2292\sqrt{29}Official answer
  2. (2)11
  3. (3)3729\sqrt{\frac{37}{29}}
  4. (4)292\frac{\sqrt{29}}{2}

Official answer

Option 1

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. 30 Jan 2024, Shift 1 · Q28If 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…MediumNumerical value
  8. 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

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.