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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Perpendicular Distance from Point to Line

JEE Main asked Perpendicular Distance from Point to Line 9 times in 9 of the 108 shifts Lumi analysed, in 2021, 2022, 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 1 year. 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
6 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, 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.

00.150.30’170’200.03’210.07’220.07’230.09’240.25’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20231 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: multi-step.

  • Distance of point from line in space
  • Triangle area from feet of perpendiculars

Difficulty

Easy 1Medium 5Hard 3

1 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. 5 Apr 2026, Shift 1 · Q13The square of the distance of the point P(5,6,7)P(5, 6, 7) from the line x−22=y−53=z−24\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4} is equal to:EasySingle correct
  2. 7 Apr 2025, Shift 2 · Q17Consider the lines L1:x−1=y−2=zL_1: x-1=y-2=z and L2:x−2=y=z−1L_2: x-2=y=z-1. Let the feet of the perpendiculars from the point P(5,1,−3)P(5,1,-3) on the lines L1L_1…MediumSingle correct
  3. 2 Apr 2025, Shift 1 · Q13Let the vertices Q and R of the triangle PQR lie on the line x+35=y−12=z+43\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, QR=5\mathrm{QR}=5 and the…MediumSingle correct
  4. 9 Apr 2024, Shift 2 · Q16Consider the line L passing through the points (1,2,3)(1, 2, 3) and (2,3,5)(2, 3, 5). The distance of the point…HardSingle correct
  5. 4 Apr 2024, Shift 2 · Q16Let P be the point of intersection of the lines x−21=y−45=z−21\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1} and…MediumSingle correct
  6. 6 Apr 2023, Shift 2 · Q16Let the line L pass through the point (0,1,2)(0, 1, 2), intersect the line x−12=y−23=z−34\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} and be parallel to the…HardSingle correct
  7. 30 Jun 2022, Shift 1 · Q28Consider a triangle ABC whose vertices are A(0,α,α)A(0, \alpha, \alpha), B(α,0,α)B(\alpha, 0, \alpha) and C(α,α,0)C(\alpha, \alpha, 0), α>0\alpha > 0. Let D…HardNumerical value
  8. 26 Jul 2022, Shift 1 · Q14The length of the perpendicular from the point (1, −2, 5)(1,\ -2,\ 5) on the line passing through (1, 2, 4)(1,\ 2,\ 4) and parallel to the line…MediumSingle correct
  9. 31 Aug 2021, Shift 2 · Q74The distance of the point (−1,2,−2)(-1, 2, -2) from the line of intersection of the planes 2x+3y+2z=02x+3y+2z = 0 and x−2y+z=0x-2y+z = 0 is :MediumSingle correct

Shifts: 31 Aug 2021, Shift 2, 30 Jun 2022, Shift 1, 26 Jul 2022, Shift 1, 6 Apr 2023, Shift 2, 4 Apr 2024, Shift 2, 9 Apr 2024, Shift 2, 2 Apr 2025, Shift 1, 7 Apr 2025, Shift 2, 5 Apr 2026, Shift 1.

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