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Saturday, 31 October

JEE Main · Maths · Vector Algebra

Simultaneous Cross and Dot Equations

JEE Main asked Simultaneous Cross and Dot Equations 7 times in 7 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024 and 2025. It belongs to Cross Product, in Vector Algebra (Maths). The longest wait between two years asking it was 1 year. In 2024 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 7 shifts
Years
5 of 8
First asked
2021
last in 2025
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.03’210.04’220.07’230.09’240.25’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 2 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
  • 20252 of 8
  • 20242 of 18
  • 20231 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

Numerical value is the usual form. Skill tested: multi-step.

  • Unknown vector from cross and dot conditions
  • Vector from cross and dot conditions

Difficulty

Easy 0Medium 4Hard 3

5 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. 3 Apr 2025, Shift 2 · Q24Let a⃗=i^+2j^+k^,b⃗=3i^−3j^+3k^,c⃗=2i^−j^+2k^\vec{a} = \hat{i} + 2\hat{j} + \hat{k}, \vec{b} = 3\hat{i} - 3\hat{j} + 3\hat{k}, \vec{c} = 2\hat{i} - \hat{j} + 2\hat{k} and…MediumNumerical value
  2. 2 Apr 2025, Shift 2 · Q16Let a⃗=2i^−3j^+k^\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}, b⃗=3i^+2j^+5k^\vec{b} = 3\hat{i} + 2\hat{j} + 5\hat{k} and a vector c⃗\vec{c} be such that…MediumSingle correct
  3. 8 Apr 2024, Shift 1 · Q28Let a⃗=9i^−13j^+25k^\vec{a}=9\hat{i}-13\hat{j}+25\hat{k}, b⃗=3i^+7j^−13k^\vec{b}=3\hat{i}+7\hat{j}-13\hat{k} and c⃗=17i^−2j^+k^\vec{c}=17\hat{i}-2\hat{j}+\hat{k} be three given…HardNumerical value
  4. 6 Apr 2024, Shift 1 · Q29Let a⃗=2i^−3j^+4k^\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}, b⃗=3i^+4j^−5k^\vec{b}=3\hat{i}+4\hat{j}-5\hat{k} and a vector c⃗\vec{c} be such that…HardNumerical value
  5. 13 Apr 2023, Shift 1 · Q9Let a⃗=i^+4j^+2k^\vec{a}=\hat{i}+4\hat{j}+2\hat{k}, b⃗=3i^−2j^+7k^\vec{b}=3\hat{i}-2\hat{j}+7\hat{k} and c⃗=2i^−j^+4k^\vec{c}=2\hat{i}-\hat{j}+4\hat{k}. If a vector…MediumSingle correct
  6. 25 Jun 2022, Shift 2 · Q26Let b⃗=i^+j^+λk^\vec{b} = \hat{i} + \hat{j} + \lambda\hat{k}, λ∈R\lambda \in \mathbb{R}. If a⃗\vec{a} is a vector such that…HardNumerical value
  7. 4 Aug 2021, Shift 2 · Q85Let a⃗=−i^+j^\vec a=-\hat i+\hat j and b⃗=i^+j^−k^\vec b=\hat i+\hat j-\hat k be two given vectors. If a vector c⃗\vec c satisfies…MediumNumerical value

Shifts: 4 Aug 2021, Shift 2, 25 Jun 2022, Shift 2, 13 Apr 2023, Shift 1, 6 Apr 2024, Shift 1, 8 Apr 2024, Shift 1, 2 Apr 2025, Shift 2, 3 Apr 2025, Shift 2.

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