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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Foot of Perpendicular

JEE Main asked Foot of Perpendicular 5 times in 5 of the 108 shifts Lumi analysed, in 2021, 2022 and 2023. It belongs to Point-Plane Distance, in Three Dimensional Geometry (Maths). The longest wait between two years asking it was 1 year. In 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
3 of 8
First asked
2021
last in 2023
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210.11’220.07’230’240’250’26

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

Shift by shift

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

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20231 of 12
  • 20223 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

Numerical value is the usual form. Skill tested: multi-step.

  • Distance between feet of perpendiculars
  • Locus of foot of perpendicular

Difficulty

Easy 0Medium 2Hard 3

3 of the 5 questions had a numerical answer.

Every question

All 5 questions

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

  1. 10 Apr 2023, Shift 2 · Q29Let the foot of perpendicular from the point A (4,3,1)(4, 3, 1) on the plane P : x−y+2z+3=0x - y + 2z + 3 = 0 be N. If B(5,α,β)(5, \alpha, \beta),…HardNumerical value
  2. 29 Jun 2022, Shift 1 · Q23Let dd be the distance between the foot of perpendiculars of the points P(1,2,−1)P(1, 2, -1) and Q(2,−1,3)Q(2, -1, 3) on the plane −x+y+z=1-x + y + z = 1.…MediumNumerical value
  3. 29 Jul 2022, Shift 2 · Q14Let QQ be the foot of perpendicular drawn from the point P (1,2,3)P\,(1, 2, 3) to the plane x+2y+z=14x+2y+z=14. If RR is a point on the plane such…MediumSingle correct
  4. 28 Jul 2022, Shift 1 · Q16The foot of the perpendicular from a point on the circle x2+y2=1, z=0x^2+y^2=1,\ z=0 to the plane 2x+3y+z=62x+3y+z=6 lies on which one of the following…HardSingle correct
  5. 26 Aug 2021, Shift 2 · Q89Let Q be the foot of the perpendicular from the point P(7,−2,13)\mathrm{P}(7,-2,13) on the plane containing the lines…HardNumerical value

Shifts: 26 Aug 2021, Shift 2, 29 Jun 2022, Shift 1, 28 Jul 2022, Shift 1, 29 Jul 2022, Shift 2, 10 Apr 2023, Shift 2.

Same topic

Other ideas in Point-Plane Distance

Point-Plane Distance has 7 ideas JEE Main has asked; 4 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas