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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Direction of Line of Intersection

JEE Main asked Direction of Line of Intersection 4 times in 4 of the 108 shifts Lumi analysed, all in 2022. It belongs to Planes in 3D, in Three Dimensional Geometry (Maths). In 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
1 of 8
First asked
2022
the only year
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200’210.14’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 4 in 24 shifts · 2023: 0 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
  • 20230 of 12
  • 20224 of 24
  • 20210 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.

  • Direction ratios of line of intersection of planes
  • Direction cosines of line of intersection of planes

Difficulty

Easy 0Medium 3Hard 1

1 of the 4 questions had a numerical answer.

Every question

All 4 questions

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

  1. 29 Jun 2022, Shift 1 · Q29Let P1:r⃗⋅(2i^+j^−3k^)=4P_1: \vec{r}\cdot(2\hat{i} + \hat{j} - 3\hat{k}) = 4 be a plane. Let P2P_2 be another plane which passes through the points…MediumNumerical value
  2. 28 Jun 2022, Shift 1 · Q15If two distinct points Q, R lie on the line of intersection of the planes −x+2y−z=0-x+2y-z=0 and 3x−5y+2z=03x-5y+2z=0 and PQ=PR=18PQ=PR=\sqrt{18} where the…HardSingle correct
  3. 27 Jul 2022, Shift 2 · Q15If the line of intersection of the planes ax+by=3ax + by = 3 and ax+by+cz=0ax + by + cz = 0, a > 0 makes an angle 30∘30^\circ with the plane…MediumSingle correct
  4. 26 Jul 2022, Shift 2 · Q15A vector a⃗\vec{a} is parallel to the line of intersection of the plane determined by the vectors i^, i^+j^\hat{i},\ \hat{i}+\hat{j} and the…MediumSingle correct

Shifts: 28 Jun 2022, Shift 1, 29 Jun 2022, Shift 1, 26 Jul 2022, Shift 2, 27 Jul 2022, 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