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Saturday, 31 October

JEE Main · Maths · Vector Algebra

Angle Between Vectors

JEE Main asked Angle Between Vectors 6 times in 5 of the 108 shifts Lumi analysed, in 2020, 2021, 2024 and 2026. It belongs to Dot Product, in Vector Algebra (Maths). The longest wait between two years asking it was 3 years. In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 5 shifts
Years
4 of 8
First asked
2020
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170.08’200.03’210’220’230.14’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 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
  • 202422 of 18
  • 20230 of 12
  • 20220 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

Single correct is the usual form. Skill tested: multi-step.

  • Vectors rotation angle then trig value
  • Unit vector from angles with two vectors

Difficulty

Easy 1Medium 3Hard 2

1 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 2 Apr 2026, Shift 2 · Q16Two adjacent sides of a parallelogram PQRSPQRS are given by PQ⃗=j^+k^\vec{PQ} = \hat{j} + \hat{k} and PS⃗=i^−j^\vec{PS} = \hat{i} - \hat{j}. If the side…MediumSingle correct
  2. 4 Apr 2024, Shift 2 · Q17Let a⃗=i^+j^+k^, b⃗=2i^+4j^−5k^\vec a=\hat i+\hat j+\hat k,\ \vec b=2\hat i+4\hat j-5\hat k and c⃗=xi^+2j^+3k^, x∈R\vec c=x\hat i+2\hat j+3\hat k,\ x\in\mathbb{R}. If d⃗\vec d is…MediumSingle correct
  3. 4 Apr 2024, Shift 2 · Q18For λ>0\lambda>0, let θ\theta be the angle between the vectors a⃗=i^+λj^−3k^\vec a=\hat i+\lambda\hat j-3\hat k and b⃗=3i^−j^+2k^\vec b=3\hat i-\hat j+2\hat k.…EasySingle correct
  4. 4 Apr 2024, Shift 1 · Q18Let a unit vector which makes an angle of 60∘60^\circ with 2i^+2j^−k^2\hat{i}+2\hat{j}-\hat{k} and an angle of 45∘45^\circ with i^−k^\hat{i}-\hat{k} be…HardSingle correct
  5. 25 Jul 2021, Shift 2 · Q88If (a⃗+3b⃗)\left(\vec{a}+3\vec{b}\right) is perpendicular to (7a⃗−5b⃗)\left(7\vec{a}-5\vec{b}\right) and (a⃗−4b⃗)\left(\vec{a}-4\vec{b}\right) is…MediumNumerical value
  6. 3 Sep 2020, Shift 2 · Q69Let a, b, c∈Rc \in \mathbf{R} be such that a2+b2+c2=1a^2 + b^2 + c^2 = 1. If…HardSingle correct

Shifts: 3 Sep 2020, Shift 2, 25 Jul 2021, Shift 2, 4 Apr 2024, Shift 2, 4 Apr 2024, Shift 1, 2 Apr 2026, Shift 2.

Same topic

Other ideas in Dot Product

Dot Product has 16 ideas JEE Main has asked; 4 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas