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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Line Perpendicular to Two Given Lines

JEE Main asked Line Perpendicular to Two Given Lines 7 times in 7 of the 108 shifts Lumi analysed, in 2021, 2023, 2024, 2025 and 2026. It belongs to Lines in 3D, in Three Dimensional Geometry (Maths). The longest wait between two years asking it was 2 years. In 2024 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 7 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, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.03’210’220.07’230.09’240.13’250.22’26

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

Shift by shift

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

  • 20262 of 9
  • 20251 of 8
  • 20242 of 18
  • 20231 of 12
  • 20220 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: multi-step.

  • Point on line at given distance
  • Foot of perpendicular with line normal to two vectors

Difficulty

Easy 0Medium 5Hard 2

3 of the 7 questions had a numerical answer.

Every question

All 7 questions

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

  1. 8 Apr 2026, Shift 2 · Q23Let a line L1L_1 pass through the origin and be perpendicular to the lines…MediumNumerical value
  2. 2 Apr 2026, Shift 1 · Q15Let a line L passing through the point (1,1,1)(1, 1, 1) be perpendicular to both the vectors 2i^+2j^+k^2\hat i+2\hat j+\hat k and…MediumSingle correct
  3. 7 Apr 2025, Shift 2 · Q16If the equation of the line passing through the point (0,−12,0)\left(0,-\frac{1}{2},0\right) and perpendicular to the lines…MediumSingle correct
  4. 31 Jan 2024, Shift 1 · Q15The distance of the point Q(0,2,−2)Q(0,2,-2) form the line passing through the point P(5,−4,3)P(5,-4,3) and perpendicular to the lines…MediumSingle correct
  5. 30 Jan 2024, Shift 2 · Q17Let L1:r⃗=(i^−j^+2k^)+λ(i^−j^+2k^),λ∈RL_1: \vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \lambda(\hat{i} - \hat{j} + 2\hat{k}), \lambda \in \mathbb{R},…MediumSingle correct
  6. 11 Apr 2023, Shift 1 · Q22Let a line ll pass through the origin and be perpendicular to the lines…HardNumerical value
  7. 25 Feb 2021, Shift 2 · Q88A line ‘ll’ passing through origin is perpendicular to the lines l1:r⃗=(3+t)i^+(−1+2t)j^+(4+2t)k^l_1: \vec{r} = (3+t)\hat{i} + (-1+2t)\hat{j} + (4+2t)\hat{k}…HardNumerical value

Shifts: 25 Feb 2021, Shift 2, 11 Apr 2023, Shift 1, 30 Jan 2024, Shift 2, 31 Jan 2024, Shift 1, 7 Apr 2025, Shift 2, 2 Apr 2026, Shift 1, 8 Apr 2026, Shift 2.

Same topic

Other ideas in Lines in 3D

Lines in 3D has 18 ideas JEE Main has asked; 10 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas