Learn

Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Foot of the Perpendicular

JEE Main asked Foot of the Perpendicular 12 times in 12 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 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 2021, 2024 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
12
in 12 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.08’200.14’210.04’220.07’230.14’240’250.22’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 4 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 3 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20243 of 18
  • 20231 of 12
  • 20221 of 24
  • 20214 of 24
  • 20201 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.

  • Foot of perpendicular on line of intersection of planes
  • Foot of perpendicular with midpoint condition

Difficulty

Easy 0Medium 12Hard 0

2 of the 12 questions had a numerical answer.

Every question

All 12 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 2 · Q14Let a triangle PQR be such that P and Q lie on the line x+38=y−42=z+12\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2} and are at a distance of 6 units from…MediumSingle correct
  2. 2 Apr 2026, Shift 2 · Q15Let the point AA be the foot of perpendicular drawn from the point P(a,b,0)P(a, b, 0) on the line…MediumSingle correct
  3. 31 Jan 2024, Shift 1 · Q29Let Q and R be the feet of perpendiculars from the point P(a,a,a)P(a,a,a) on the lines x=y, z=1x=y,\ z=1 and x=−y, z=−1x=-y,\ z=-1 respectively. If…MediumNumerical value
  4. 30 Jan 2024, Shift 1 · Q16Let (α,β,γ)(\alpha,\beta,\gamma) be the foot of perpendicular from the point (1,2,3)(1,2,3) on the line x+35=y−12=z+43\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}.…MediumSingle correct
  5. 6 Apr 2024, Shift 1 · Q28Let PP be the point (10,−2,−1)(10,-2,-1) and QQ be the foot of the perpendicular drawn from the point R(1,7,6)R(1,7,6) on the line passing through the…MediumNumerical value
  6. 13 Apr 2023, Shift 2 · Q16Let N be the foot of perpendicular from the point P (1,−2,3)(1,-2,3) on the line passing through the points (4,5,8)(4,5,8) and (1,−7,5)(1,-7,5). Then the…MediumSingle correct
  7. 27 Jun 2022, Shift 2 · Q13Let the foot of the perpendicular from the point (1,2,4)(1, 2, 4) on the line x+24=y−12=z+13\frac{x+2}{4}=\frac{y-1}{2}=\frac{z+1}{3} be PP. Then the…MediumSingle correct
  8. 16 Mar 2021, Shift 2 · Q61If the foot of the perpendicular from point (4, 3, 8) on the line L1:x−al=y−23=z−b4L_1:\frac{x-a}{l}=\frac{y-2}{3}=\frac{z-b}{4}, l≠0l\neq0 is (3, 5, 7),…MediumSingle correct
  9. 25 Jul 2021, Shift 1 · Q69Let the foot of perpendicular from a point P(1, 2, −1-1) to the straight line L:x1=y0=z−1L:\frac{x}{1}=\frac{y}{0}=\frac{z}{-1} be N. Let a line be…MediumSingle correct
  10. 22 Jul 2021, Shift 2 · Q69Let L\mathrm{L} be the line of intersection of planes r⃗⋅(i^−j^+2k^)=2\vec{\mathrm{r}}\cdot(\hat{i}-\hat{j}+2\hat{k})=2 and…MediumSingle correct
  11. 26 Feb 2021, Shift 2 · Q76Let L be a line obtained from the intersection of two planes x+2y+z=6x+2y+z=6 and y+2z=4y+2z=4. If point P(α,β,γ)P(\alpha, \beta, \gamma) is the foot of…MediumSingle correct
  12. 3 Sep 2020, Shift 1 · Q65The foot of the perpendicular drawn from the point (4, 2, 3) to the line joining the points (1, −2-2, 3) and (1, 1, 0) lies on the plane :MediumSingle correct

Shifts: 3 Sep 2020, Shift 1, 26 Feb 2021, Shift 2, 16 Mar 2021, Shift 2, 22 Jul 2021, Shift 2, 25 Jul 2021, Shift 1, 27 Jun 2022, Shift 2, 13 Apr 2023, Shift 2, 30 Jan 2024, Shift 1, 31 Jan 2024, Shift 1, 6 Apr 2024, Shift 1, 2 Apr 2026, Shift 2, 5 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