Learn

Saturday, 31 October

JEE Main · Maths · Vector Algebra

Solving for Unknown in Coplanarity

JEE Main asked Solving for Unknown in Coplanarity 7 times in 7 of the 108 shifts Lumi analysed, in 2020, 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 2021, 2022 and 2023 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 7 shifts
Years
4 of 8
First asked
2020
last in 2023
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170.08’200.07’210.07’220.14’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 2 in 24 shifts · 2023: 2 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
  • 20232 of 12
  • 20222 of 24
  • 20212 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.

  • Coplanarity of three vectors with parameters
  • Coplanar vectors with unknown scalars

Difficulty

Easy 0Medium 6Hard 1

2 of the 7 questions had a numerical answer.

Every question

All 7 questions

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

  1. 15 Apr 2023, Shift 1 · Q16Let SS be the set of all (λ,μ)(\lambda,\mu) for which the vectors λi^−j^+k^\lambda\hat{i}-\hat{j}+\hat{k}, i^+2j^+μk^\hat{i}+2\hat{j}+\mu\hat{k} and…MediumSingle correct
  2. 12 Apr 2023, Shift 1 · Q16Let a,b,ca, b, c be three distinct real numbers, none equal to one. If the vectors ai^+j^+k^a\hat{i}+\hat{j}+\hat{k}, i^+bj^+k^\hat{i}+b\hat{j}+\hat{k} and…MediumSingle correct
  3. 30 Jun 2022, Shift 1 · Q17Let a vector c⃗\vec{c} be coplanar with the vectors a⃗=−i^+j^+k^\vec{a} = -\hat{i} + \hat{j} + \hat{k} and b⃗=2i^+j^−k^\vec{b} = 2\hat{i} + \hat{j} - \hat{k}.…HardSingle correct
  4. 28 Jun 2022, Shift 1 · Q24If a⃗=2i^+j^+3k^\vec{a}=2\hat{i}+\hat{j}+3\hat{k}, b⃗=3i^+3j^+k^\vec{b}=3\hat{i}+3\hat{j}+\hat{k} and c⃗=c1i^+c2j^+c3k^\vec{c}=c_1\hat{i}+c_2\hat{j}+c_3\hat{k} are coplanar…MediumNumerical value
  5. 25 Jul 2021, Shift 2 · Q80Let a, b and c be distinct positive numbers. If the vectors ai^+aj^+ck^a\hat{i}+a\hat{j}+c\hat{k}, i^+k^\hat{i}+\hat{k} and…MediumSingle correct
  6. 25 Jul 2021, Shift 1 · Q71Let the vectors (2+a+b)i^+(a+2b+c)j^−(b+c)k^(2+a+b)\hat{i}+(a+2b+c)\hat{j}-(b+c)\hat{k}, (1+b)i^+2bj^−bk^(1+b)\hat{i}+2b\hat{j}-b\hat{k} and…MediumSingle correct
  7. 9 Jan 2020, Shift 1 · Q73If the vectors, p⃗=(a+1)i^+aj^+ak^\vec{p}=(a+1)\hat{i}+a\hat{j}+a\hat{k}, q⃗=ai^+(a+1)j^+ak^\vec{q}=a\hat{i}+(a+1)\hat{j}+a\hat{k} and…MediumNumerical value

Shifts: 9 Jan 2020, Shift 1, 25 Jul 2021, Shift 2, 25 Jul 2021, Shift 1, 28 Jun 2022, Shift 1, 30 Jun 2022, Shift 1, 12 Apr 2023, Shift 1, 15 Apr 2023, Shift 1.

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