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Saturday, 31 October

JEE Main · Maths · Vector Algebra

Lagrange's Identity

JEE Main asked Lagrange's Identity 8 times in 7 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023 and 2024. It belongs to Cross Product, in Vector Algebra (Maths). The longest wait between two years asking it was 1 year. In 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
8
in 7 shifts
Years
5 of 8
First asked
2020
last in 2024
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170.08’200.03’210.11’220.07’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 3 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20231 of 12
  • 202222 of 24
  • 20211 of 24
  • 20201 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: calculation.

  • Unknown vector from cross and dot conditions
  • Vector magnitudes from dot product and angle

Difficulty

Easy 1Medium 6Hard 1

4 of the 8 questions had a numerical answer.

Every question

All 8 questions

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

  1. 31 Jan 2024, Shift 1 · Q30Let a⃗\vec{a} and b⃗\vec{b} be two vectors such that ∣a⃗∣=1, ∣b⃗∣=4|\vec{a}|=1,\ |\vec{b}|=4, and a⃗⋅b⃗=2\vec{a}\cdot\vec{b}=2. If…MediumNumerical value
  2. 30 Jan 2024, Shift 2 · Q19Let a⃗=i^+αj^+βk^\vec{a} = \hat{i} + \alpha\hat{j} + \beta\hat{k}, α,β∈R\alpha, \beta \in \mathbb{R}. Let a vector b⃗\vec{b} be such that the angle…MediumSingle correct
  3. 6 Apr 2023, Shift 1 · Q16Let a⃗=2i^+3j^+4k^\vec a=2\hat i+3\hat j+4\hat k, b⃗=i^−2j^−2k^\vec b=\hat i-2\hat j-2\hat k and c⃗=−i^+4j^+3k^\vec c=-\hat i+4\hat j+3\hat k. If d⃗\vec d is a vector…MediumSingle correct
  4. 25 Jun 2022, Shift 1 · Q23Let θ\theta be the angle between the vectors a⃗\vec{a} and b⃗\vec{b}, where ∣a⃗∣=4|\vec{a}|=4, ∣b⃗∣=3|\vec{b}|=3 and…MediumNumerical value
  5. 29 Jul 2022, Shift 2 · Q18Let a⃗,b⃗,c⃗\vec{a},\vec{b},\vec{c} be three coplanar concurrent vectors such that angles between any two of them is same. If the product of…HardSingle correct
  6. 29 Jul 2022, Shift 2 · Q29Let a⃗\vec{a} and b⃗\vec{b} be two vectors such that ∣a⃗+b⃗∣2=∣a⃗∣2+2∣b⃗∣2|\vec{a}+\vec{b}|^2=|\vec{a}|^2+2|\vec{b}|^2, a⃗⋅b⃗=3\vec{a}\cdot\vec{b}=3 and…MediumNumerical value
  7. 25 Jul 2021, Shift 2 · Q78If ∣a⃗∣=2|\vec{a}|=2, ∣b⃗∣=5|\vec{b}|=5 and ∣a⃗×b⃗∣=8|\vec{a}\times\vec{b}|=8, then ∣a⃗⋅b⃗∣|\vec{a}\cdot\vec{b}| is equal to :EasySingle correct
  8. 2 Sep 2020, Shift 2 · Q73Let the position vectors of points 'A' and 'B' be i^+j^+k^\hat{i}+\hat{j}+\hat{k} and 2i^+j^+3k^2\hat{i}+\hat{j}+3\hat{k}, respectively. A point 'P'…MediumNumerical value

Shifts: 2 Sep 2020, Shift 2, 25 Jul 2021, Shift 2, 25 Jun 2022, Shift 1, 29 Jul 2022, Shift 2, 6 Apr 2023, Shift 1, 30 Jan 2024, Shift 2, 31 Jan 2024, Shift 1.

Same topic

Other ideas in Cross Product

Cross Product has 13 ideas JEE Main has asked; 9 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas