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Saturday, 31 October

JEE Main · Maths · Vector Algebra

Magnitude and Sine Formula

JEE Main asked Magnitude and Sine Formula 13 times in 13 of the 108 shifts Lumi analysed, in 2017, 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 3 years, across 2018 and 2019, which Lumi has no shifts for. In 2021, 2022, 2023 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
13
in 13 shifts
Years
7 of 8
First asked
2017
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2017, 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.

00.510.86’170.08’200.07’210.11’220.14’230.14’240’250.11’26

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

Shift by shift

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

  • 20261 of 9
  • 20250 of 8
  • 20243 of 18
  • 20232 of 12
  • 20223 of 24
  • 20212 of 24
  • 20201 of 12
  • 20171 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
  • Express coefficient via dot products

Difficulty

Easy 0Medium 4Hard 9

3 of the 13 questions had a numerical answer.

Every question

All 13 questions

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

  1. 4 Apr 2026, Shift 2 · Q15Let u^\hat u and v^\hat v be unit vectors inclined at an acute angle such that ∣u^×v^∣=32|\hat u\times\hat v|=\frac{\sqrt3}{2}. If…HardSingle correct
  2. 30 Jan 2024, Shift 1 · Q18Let a⃗=a1i^+a2j^+a3k^\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} and b⃗=b1i^+b2j^+b3k^\vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} be two vectors such that ∣a⃗∣=1|\vec{a}|=1,…HardSingle correct
  3. 6 Apr 2024, Shift 2 · Q19Let a⃗=6i^+j^−k^\vec{a}=6\hat{i}+\hat{j}-\hat{k} and b⃗=i^+j^\vec{b}=\hat{i}+\hat{j}. If c⃗\vec{c} is a vector such that ∣c⃗∣≥6|\vec{c}|\ge 6,…HardSingle correct
  4. 5 Apr 2024, Shift 2 · Q19Consider three vectors a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c}. Let ∣a⃗∣=2|\vec{a}| = 2, ∣b⃗∣=3|\vec{b}| = 3 and a⃗=b⃗×c⃗\vec{a} = \vec{b} \times \vec{c}. If…HardSingle correct
  5. 11 Apr 2023, Shift 2 · Q29Let a⃗=i^+2j^+3k^\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k} and b⃗=i^+j^−k^\vec{b} = \hat{i} + \hat{j} - \hat{k}. If c⃗\vec{c} is a vector such that…HardNumerical value
  6. 11 Apr 2023, Shift 1 · Q11Let a⃗\vec{a} be a non-zero vector parallel to the line of intersection of the two planes described by i^+j^, i^+k^\hat{i}+\hat{j},\ \hat{i}+\hat{k}…HardSingle correct
  7. 29 Jul 2022, Shift 1 · Q14Let a^\hat{a} and b^\hat{b} be two unit vectors such that the angle between them is π4\frac{\pi}{4}. If θ\theta is the angle between the…HardSingle correct
  8. 26 Jul 2022, Shift 1 · Q15Let a→=αi^+j^−k^\overrightarrow{\mathrm{a}} = \alpha \hat{i} + \hat{j} - \hat{k} and…MediumSingle correct
  9. 25 Jul 2022, Shift 1 · Q15Let ABCABC be a triangle such that BC→=a⃗\overrightarrow{BC}=\vec a, CA→=b⃗\overrightarrow{CA}=\vec b, AB→=c⃗\overrightarrow{AB}=\vec c,…HardTwo statements
  10. 18 Mar 2021, Shift 2 · Q80Let a⃗\vec{a} and b⃗\vec{b} be two non-zero vectors perpendicular to each other and ∣a⃗∣=∣b⃗∣\left|\vec{a}\right|=\left|\vec{b}\right|. If…MediumSingle correct
  11. 27 Aug 2021, Shift 1 · Q89Let a⃗=i^+5j^+αk^\vec{a}=\hat{i}+5\hat{j}+\alpha\hat{k}, b⃗=i^+3j^+βk^\vec{b}=\hat{i}+3\hat{j}+\beta\hat{k} and c⃗=−i^+2j^−3k^\vec{c}=-\hat{i}+2\hat{j}-3\hat{k} be three…MediumNumerical value
  12. 9 Jan 2020, Shift 2 · Q75Let a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} be three vectors such that ∣a⃗∣=3|\vec{a}|=\sqrt3, ∣b⃗∣=5|\vec{b}|=5, b⃗⋅c⃗=10\vec{b}\cdot\vec{c}=10 and the…MediumNumerical value
  13. 2 Apr 2017 (offline) · Q84Let a⃗=2i^+j^−2k^\vec{a}=2\hat{i}+\hat{j}-2\hat{k} and b⃗=i^+j^\vec{b}=\hat{i}+\hat{j}. Let c⃗\vec{c} be a vector such that ∣c⃗−a⃗∣=3|\vec{c}-\vec{a}|=3,…HardSingle correct

Shifts: 2 Apr 2017 (offline), 9 Jan 2020, Shift 2, 18 Mar 2021, Shift 2, 27 Aug 2021, Shift 1, 25 Jul 2022, Shift 1, 26 Jul 2022, Shift 1, 29 Jul 2022, Shift 1, 11 Apr 2023, Shift 2, 11 Apr 2023, Shift 1, 30 Jan 2024, Shift 1, 5 Apr 2024, Shift 2, 6 Apr 2024, Shift 2, 4 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