Learn

Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Vector Shortest Distance Formula

JEE Main asked Vector Shortest Distance Formula 9 times in 9 of the 108 shifts Lumi analysed, in 2021, 2022, 2024, 2025 and 2026. It belongs to Skew Lines, in Three Dimensional Geometry (Maths). The longest wait between two years asking it was 2 years. In 2022, 2024 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
9
in 9 shifts
Years
5 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.03’210.07’220’230.14’240.25’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 3 in 18 shifts · 2025: 2 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20252 of 8
  • 20243 of 18
  • 20230 of 12
  • 20222 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Shortest distance between skew lines
  • Shortest distance between skew lines then ellipse property

Difficulty

Easy 2Medium 5Hard 2

4 of the 9 questions had a numerical answer.

Every question

All 9 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 4 Apr 2026, Shift 2 · Q13The shortest distance between the lines…EasySingle correct
  2. 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
  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. 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
  5. 6 Apr 2024, Shift 1 · Q17The shortest distance between the lines x−32=y+15−7=z−95\frac{x-3}{2}=\frac{y+15}{-7}=\frac{z-9}{5} and x+12=y−11=z−9−3\frac{x+1}{2}=\frac{y-1}{1}=\frac{z-9}{-3} isMediumSingle correct
  6. 4 Apr 2024, Shift 1 · Q29If the shortest distance between the lines x+22=y+33=z−54\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4} and x−31=y−2−3=z+42\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2} is…HardNumerical value
  7. 25 Jun 2022, Shift 2 · Q30Let l1l_1 be the line in xyxy-plane with xx and yy intercepts 18\frac{1}{8} and 142\frac{1}{4\sqrt{2}} respectively, and l2l_2 be the…HardNumerical value
  8. 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
  9. 24 Feb 2021, Shift 2 · Q88Let λ\lambda be an integer. If the shortest distance between the lines x−λ=2y−1=−2zx-\lambda=2y-1=-2z and x=y+2λ=z−λx=y+2\lambda=z-\lambda is…MediumNumerical value

Shifts: 24 Feb 2021, Shift 2, 24 Jun 2022, Shift 1, 25 Jun 2022, Shift 2, 4 Apr 2024, Shift 1, 6 Apr 2024, Shift 1, 8 Apr 2024, Shift 1, 2 Apr 2025, Shift 2, 4 Apr 2025, Shift 2, 4 Apr 2026, Shift 2.

Same topic

Other ideas in Skew Lines

Skew Lines has 8 ideas JEE Main has asked; 4 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas