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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Plane Through Three Points

JEE Main asked Plane Through Three Points 3 times in 3 of the 108 shifts Lumi analysed, in 2021 and 2023. It belongs to Planes in 3D, in Three Dimensional Geometry (Maths). The longest wait between two years asking it was 2 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
2 of 8
First asked
2021
last in 2023
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200.07’210’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 0 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
  • 20220 of 24
  • 20212 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.

  • Foot of perpendicular on line of intersection of planes
  • Distance of point from plane through three points

Difficulty

Easy 0Medium 1Hard 2

2 of the 3 questions had a numerical answer.

Every question

All 3 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 2023, Shift 2 · Q30Let P1P_1 be the plane 3x−y−7z=113x - y - 7z = 11 and P2P_2 be the plane passing through the points (2,−1,0)(2, -1, 0), (2,0,−1)(2, 0, -1), and (5,1,1)(5, 1, 1).…HardNumerical value
  2. 4 Aug 2021, Shift 1 · Q88If the distance between the point (a,−1,1)(a, -1, 1) (a>0)(a>0) and the plane passing through the points (1,−2,1)(1, -2, 1), (3,1,0)(3, 1, 0) and (2,0,1)(2, 0, 1)…MediumNumerical value
  3. 3 Aug 2021, Shift 1 · Q68A plane passes through the points A(1, 2, 3), B(3, 5, 2) and C(2, 1, 5). If P(aa, bb, cc) be a point such that a(b+c)=bca(b + c) = bc, then…HardSingle correct

Shifts: 3 Aug 2021, Shift 1, 4 Aug 2021, Shift 1, 8 Apr 2023, Shift 2.

Same topic

Other ideas in Planes in 3D

Planes in 3D has 22 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas