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Saturday, 31 October

JEE Main · Maths · Vector Algebra

Coplanarity of Four Points

JEE Main asked Coplanarity of Four Points 5 times in 5 of the 108 shifts Lumi analysed, in 2021, 2022 and 2023. It belongs to Triple Products, in Vector Algebra (Maths). The longest wait between two years asking it was 1 year. In 2023 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.

00.150.30’170’200.03’210.04’220.21’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 3 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
  • 20233 of 12
  • 20221 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: calculation.

  • Parameter values for coplanar points
  • Coplanarity of four position vectors

Difficulty

Easy 0Medium 5Hard 0

Every question was multiple choice.

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. 11 Apr 2023, Shift 2 · Q17If four distinct points with position vectors a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} and d⃗\vec{d} are coplanar, then [a⃗ b⃗ c⃗][\vec{a}\ \vec{b}\ \vec{c}]…MediumSingle correct
  2. 6 Apr 2023, Shift 2 · Q17The sum of all values of α\alpha, for which the points whose position vectors are i^−2j^+3k^\hat{i}-2\hat{j}+3\hat{k},…MediumSingle correct
  3. 6 Apr 2023, Shift 1 · Q15Let the position vectors of the points A, B, C and D be 5i^+5j^+2λk^5\hat i+5\hat j+2\lambda\hat k, i^+2j^+3k^\hat i+2\hat j+3\hat k,…MediumSingle correct
  4. 29 Jul 2022, Shift 2 · Q15If (2,3,9)(2, 3, 9), (5,2,1)(5, 2, 1), (1,λ,8)(1, \lambda, 8) and (λ,2,3)(\lambda, 2, 3) are coplanar, then the product of all possible values of λ\lambda is :MediumSingle correct
  5. 26 Feb 2021, Shift 1 · Q62If (1,5,35)(1, 5, 35), (7,5,5)(7, 5, 5), (1,λ,7)(1, \lambda, 7) and (2λ,1,2)(2\lambda, 1, 2) are coplanar, then the sum of all possible values of λ\lambda is :MediumSingle correct

Shifts: 26 Feb 2021, Shift 1, 29 Jul 2022, Shift 2, 6 Apr 2023, Shift 2, 6 Apr 2023, Shift 1, 11 Apr 2023, Shift 2.

Same topic

Other ideas in Triple Products

Triple Products has 10 ideas JEE Main has asked; 6 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas