Learn

Saturday, 31 October

JEE Main · Maths · Vector Algebra

Solving Vector Equations with Cross Products

JEE Main asked Solving Vector Equations with Cross Products 20 times in 20 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 and 2026. It belongs to Cross Product, in Vector Algebra (Maths). The longest wait between two years asking it was 2 years. In 2021, 2022, 2023, 2024 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
20
in 20 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

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

00.20.40’170.08’200.14’210.11’220.14’230.33’240’250.33’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 4 in 24 shifts · 2022: 3 in 24 shifts · 2023: 2 in 12 shifts · 2024: 7 in 18 shifts · 2025: 0 in 8 shifts · 2026: 3 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20263 of 9
  • 20250 of 8
  • 20247 of 18
  • 20232 of 12
  • 20223 of 24
  • 20214 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.

  • Unknown vector from cross and dot conditions
  • Solve vector cross product equation

Difficulty

Easy 0Medium 13Hard 7

6 of the 20 questions had a numerical answer.

Every question

All 20 questions

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

  1. 8 Apr 2026, Shift 2 · Q14Let a⃗=4i^−j^+3k^\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}, b⃗=10i^+2j^−k^\vec{b} = 10\hat{i} + 2\hat{j} - \hat{k} and a vector c⃗\vec{c} be such that…MediumSingle correct
  2. 6 Apr 2026, Shift 1 · Q23If a⃗=i^+j^+k^\vec{a}=\hat{i}+\hat{j}+\hat{k}, b⃗=j^−k^\vec{b}=\hat{j}-\hat{k} and c⃗\vec{c} be three vectors such that a⃗×c⃗=b⃗\vec{a}\times\vec{c}=\vec{b}…MediumNumerical value
  3. 5 Apr 2026, Shift 1 · Q14Let a⃗=7i^+j^−k^\vec{a} = \sqrt{7}\hat{i} + \hat{j} - \hat{k} and b⃗=j^+2k^\vec{b} = \hat{j} + 2\hat{k}. If r⃗\vec{r} is a vector such that…MediumSingle correct
  4. 31 Jan 2024, Shift 2 · Q30Let a⃗=3i^+2j^+k^\vec{a}=3\hat{i}+2\hat{j}+\hat{k}, b⃗=2i^−j^+3k^\vec{b}=2\hat{i}-\hat{j}+3\hat{k} and c⃗\vec{c} be a vector such that…HardNumerical value
  5. 31 Jan 2024, Shift 1 · Q18Let a⃗=3i^+j^−2k^\vec{a}=3\hat{i}+\hat{j}-2\hat{k}, b⃗=4i^+j^+7k^\vec{b}=4\hat{i}+\hat{j}+7\hat{k} and c⃗=i^−3j^+4k^\vec{c}=\hat{i}-3\hat{j}+4\hat{k} be three vectors. If…MediumSingle correct
  6. 27 Jan 2024, Shift 1 · Q19Let a⃗=i^+2j^+k^\vec{a}=\hat{i}+2\hat{j}+\hat{k}, b⃗=3(i^−j^+k^)\vec{b}=3(\hat{i}-\hat{j}+\hat{k}). Let c⃗\vec{c} be the vector such that…MediumSingle correct
  7. 9 Apr 2024, Shift 2 · Q17Between the following two statements: Statement I : Let a⃗=i^+2j^−3k^\vec{a}=\hat{i}+2\hat{j}-3\hat{k} and b⃗=2i^+j^−k^\vec{b}=2\hat{i}+\hat{j}-\hat{k}. Then…HardTwo statements
  8. 8 Apr 2024, Shift 2 · Q17Let a⃗=4i^−j^+k^\vec{a} = 4\hat{i} - \hat{j} + \hat{k}, b⃗=11i^−j^+k^\vec{b} = 11\hat{i} - \hat{j} + \hat{k} and c⃗\vec{c} be a vector such that…HardSingle correct
  9. 5 Apr 2024, Shift 2 · Q18Let a⃗=2i^+5j^−k^\vec{a} = 2\hat{i}+5\hat{j}-\hat{k}, b⃗=2i^−2j^+2k^\vec{b} = 2\hat{i}-2\hat{j}+2\hat{k} and c⃗\vec{c} be three vectors such that…MediumSingle correct
  10. 5 Apr 2024, Shift 1 · Q29Let a⃗=i^−3j^+7k^\vec a=\hat i-3\hat j+7\hat k, b⃗=2i^−j^+k^\vec b=2\hat i-\hat j+\hat k and c⃗\vec c be a vector such that…MediumNumerical value
  11. 13 Apr 2023, Shift 1 · Q28Let a⃗=3i^+j^−k^\vec{a}=3\hat{i}+\hat{j}-\hat{k} and c⃗=2i^−3j^+3k^\vec{c}=2\hat{i}-3\hat{j}+3\hat{k}. If b⃗\vec{b} is a vector such that…MediumNumerical value
  12. 8 Apr 2023, Shift 1 · Q29Let a⃗=6i^+9j^+12k^\vec{a}=6\hat{i}+9\hat{j}+12\hat{k}, b⃗=αi^+11j^−2k^\vec{b}=\alpha\hat{i}+11\hat{j}-2\hat{k} and c⃗\vec{c} be vectors such that…HardNumerical value
  13. 28 Jun 2022, Shift 2 · Q19Let a⃗\vec{a} be a vector which is perpendicular to the vector 3i^+12j^+2k^3\hat{i}+\frac{1}{2}\hat{j}+2\hat{k}. If…HardSingle correct
  14. 27 Jun 2022, Shift 1 · Q15Let a⃗=i^+j^−k^\vec{a}=\hat{i}+\hat{j}-\hat{k} and c⃗=2i^−3j^+2k^\vec{c}=2\hat{i}-3\hat{j}+2\hat{k}. Then the number of vectors b⃗\vec{b} such that…MediumSingle correct
  15. 24 Jun 2022, Shift 1 · Q16Let a^,b^\hat{a}, \hat{b} be unit vectors. If c⃗\vec{c} be a vector such that the angle between a^\hat{a} and c⃗\vec{c} is π12\frac{\pi}{12},…HardSingle correct
  16. 17 Mar 2021, Shift 1 · Q78Let a⃗=2i^−3j^+4k^\vec{a}=2\hat{i}-3\hat{j}+4\hat{k} and b⃗=7i^+j^−6k^\vec{b}=7\hat{i}+\hat{j}-6\hat{k}. If r⃗×a⃗=r⃗×b⃗\vec{r}\times\vec{a}=\vec{r}\times\vec{b},…MediumSingle correct
  17. 16 Mar 2021, Shift 2 · Q63Let a⃗=i^+2j^−3k^\vec a=\hat i+2\hat j-3\hat k and b⃗=2i^−3j^+5k^\vec b=2\hat i-3\hat j+5\hat k. If r⃗×a⃗=b⃗×r⃗\vec r\times\vec a=\vec b\times\vec r,…HardSingle correct
  18. 25 Feb 2021, Shift 1 · Q90Let a⃗=i^+2j^−k^\vec{a} = \hat{i} + 2\hat{j} - \hat{k}, b⃗=i^−j^\vec{b} = \hat{i} - \hat{j} and c⃗=i^−j^−k^\vec{c} = \hat{i} - \hat{j} - \hat{k} be three given…MediumNumerical value
  19. 26 Aug 2021, Shift 1 · Q77Let a⃗=i^+j^+k^\vec{a}=\hat{i}+\hat{j}+\hat{k} and b⃗=j^−k^\vec{b}=\hat{j}-\hat{k}. If c⃗\vec{c} is a vector such that a⃗×c⃗=b⃗\vec{a}\times\vec{c}=\vec{b} and…MediumSingle correct
  20. 8 Jan 2020, Shift 2 · Q67Let a⃗=i^−2j^+k^\vec{a} = \hat{i} - 2\hat{j} + \hat{k} and b⃗=i^−j^+k^\vec{b} = \hat{i} - \hat{j} + \hat{k} be two vectors. If c⃗\vec{c} is a vector such…MediumSingle correct

Shifts: 8 Jan 2020, Shift 2, 25 Feb 2021, Shift 1, 16 Mar 2021, Shift 2, 17 Mar 2021, Shift 1, 26 Aug 2021, Shift 1, 24 Jun 2022, Shift 1, 27 Jun 2022, Shift 1, 28 Jun 2022, Shift 2, 8 Apr 2023, Shift 1, 13 Apr 2023, Shift 1, 27 Jan 2024, Shift 1, 31 Jan 2024, Shift 2, 31 Jan 2024, Shift 1, 5 Apr 2024, Shift 2, 5 Apr 2024, Shift 1, 8 Apr 2024, Shift 2, 9 Apr 2024, Shift 2, 5 Apr 2026, Shift 1, 6 Apr 2026, Shift 1, 8 Apr 2026, 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