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Saturday, 10 October

JEE Main Maths · Three Dimensional Geometry

Skew Lines in JEE Main

Skew Lines (Maths, Three Dimensional Geometry) came 15 times in 15 of the 42 JEE Main shifts Lumi analysed, across 6 distinct ideas. 11 of them came in 2024–26; it was last asked in 2026.

Questions
15
in 15 shifts
Ideas asked
6
3 asked more than once
Numerical answer
2
13% of its questions
Pattern
Asked most years
last asked 2026
Questions each year
0360’171’200’211’222’234’245’252’26

In the shifts Lumi analysed for each year.

Difficulty and format
Easy 4Medium 10Hard 1

Format

  • Single correct13 Q
  • Numerical value2 Q
Ideas inside the topic
6 ideas
Where it sits

Part of Three Dimensional Geometry, which had 84 questions in all. Skew Lines accounts for 18% of them. In Lumi's JEE taxonomy it belongs to Vectors and 3D Geometry.

Every question

All 15 Skew Lines questions

Newest first, each with its options and official answer.

  1. 4 Apr 2026, Shift 2 · Q13The shortest distance between the lines…EasySingle correct
  2. 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
  3. 2 Apr 2025, Shift 2 · Q15The line L1L_1 is parallel to the vector a⃗=−3i^+2j^+4k^\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k} and passes through the point (7,6,2)(7, 6, 2) and the line…EasySingle correct
  4. 3 Apr 2025, Shift 1 · Q14Line L1\mathrm{L}_1 passes through the point (1,2,3)(1, 2, 3) and is parallel to zz-axis. Line L2\mathrm{L}_2 passes through the point…MediumSingle correct
  5. 4 Apr 2025, Shift 2 · Q14Let the values of p, for which the shortest distance between the lines x+13=y4=z5\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5} and…MediumSingle correct
  6. 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
  7. 8 Apr 2025, Shift 2 · Q15Let the values of λ\lambda for which 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…HardSingle correct
  8. 6 Apr 2024, Shift 2 · Q28If the shortest distance between the lines x−λ3=y−2−1=z−11\frac{x-\lambda}{3}=\frac{y-2}{-1}=\frac{z-1}{1} and…MediumNumerical value
  9. 8 Apr 2024, Shift 1 · Q14If the shortest distance between the lines L1:r⃗=(2+λ)i^+(1−3λ)j^+(3+4λ)k^L_1:\vec{r}=(2+\lambda)\hat{i}+(1-3\lambda)\hat{j}+(3+4\lambda)\hat{k},…MediumSingle correct
  10. 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
  11. 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
  12. 6 Apr 2023, Shift 1 · Q14One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges along xx, yy and zz axes are 3, 4 and 5…MediumSingle correct
  13. 13 Apr 2023, Shift 2 · Q15The line, that is coplanar to the line x+3−3=y−11=z−55\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}, isMediumSingle correct
  14. 24 Jun 2022, Shift 1 · Q30If the shortest distance between the lines r⃗=(−i^+3k^)+λ(i^−aj^)\vec{r}=(-\hat{i}+3\hat{k})+\lambda(\hat{i}-a\hat{j}) and…MediumNumerical value
  15. 8 Jan 2020, Shift 1 · Q65The shortest distance between the lines x−33=y−8−1=z−31\dfrac{x-3}{3}=\dfrac{y-8}{-1}=\dfrac{z-3}{1} and…MediumSingle correct