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Saturday, 31 October

JEE Main · Maths · Vector Algebra

Scalar and Vector Projection

JEE Main asked Scalar and Vector Projection 11 times in 11 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2024 and 2025. It belongs to Dot Product, in Vector Algebra (Maths). The longest wait between two years asking it was 2 years. In 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
11
in 11 shifts
Years
5 of 8
First asked
2020
last in 2025
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200.10’210.14’220’230.09’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 3 in 24 shifts · 2022: 4 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20242 of 18
  • 20230 of 12
  • 20224 of 24
  • 20213 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
  • Vector from equal projections on given vectors

Difficulty

Easy 2Medium 7Hard 2

4 of the 11 questions had a numerical answer.

Every question

All 11 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 2025, Shift 1 · Q11If a⃗\vec{a} is a nonzero vector such that its projections on the vectors 2i^−j^+2k^2\hat{i}-\hat{j}+2\hat{k}, i^+2j^−2k^\hat{i}+2\hat{j}-2\hat{k} and…MediumSingle correct
  2. 1 Feb 2024, Shift 2 · Q17Consider a ΔABC\Delta ABC where A(1,3,2)A(1,3,2), B(−2,8,0)B(-2,8,0) and C(3,6,7)C(3,6,7). If the angle bisector of ∠BAC\angle BAC meets the line BCBC at DD,…MediumSingle correct
  3. 8 Apr 2024, Shift 2 · Q18Let a⃗=i^+2j^+3k^\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}, b⃗=2i^+3j^−5k^\vec{b} = 2\hat{i} + 3\hat{j} - 5\hat{k} and…MediumSingle correct
  4. 29 Jun 2022, Shift 1 · Q5Let a⃗=αi^+3j^−k^\vec{a} = \alpha\hat{i} + 3\hat{j} - \hat{k}, b⃗=3i^−βj^+4k^\vec{b} = 3\hat{i} - \beta\hat{j} + 4\hat{k} and…MediumSingle correct
  5. 26 Jun 2022, Shift 2 · Q16Let a⃗=i^+j^+2k^\vec{a} = \hat{i} + \hat{j} + 2\hat{k}, b⃗=2i^−3j^+k^\vec{b} = 2\hat{i} - 3\hat{j} + \hat{k} and c⃗=i^−j^+k^\vec{c} = \hat{i} - \hat{j} + \hat{k} be…MediumSingle correct
  6. 30 Jul 2022, Shift 2 · Q88Let OABCOABC be a parallelogram, OO be the origin, A (2,4,−5)A\,(2, 4, -5) and C (b,2,3)C\,(b, 2, 3). If P (a,a,a)P\,(a, a, a) and Q (9−a2,3,a−1)Q\,(9-a^2, 3, a-1),…HardNumerical value
  7. 25 Jul 2022, Shift 2 · Q17Let a⃗=i^−j^+2k^\vec{a}=\hat{i}-\hat{j}+2\hat{k} and let b⃗\vec{b} be a vector such that a⃗×b⃗=2i^−k^\vec{a}\times\vec{b}=2\hat{i}-\hat{k} and…MediumSingle correct
  8. 18 Mar 2021, Shift 2 · Q66In a triangle ABC, if ∣BC→∣=8\left|\overrightarrow{BC}\right|=8, ∣CA→∣=7\left|\overrightarrow{CA}\right|=7, ∣AB→∣=10\left|\overrightarrow{AB}\right|=10,…MediumSingle correct
  9. 17 Mar 2021, Shift 2 · Q89Let x→\overrightarrow{x} be a vector in the plane containing vectors a→=2i^−j^+k^\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k} and…HardNumerical value
  10. 26 Aug 2021, Shift 2 · Q87If the projection of the vector i^+2j^+k^\hat{i}+2\hat{j}+\hat{k} on the sum of the two vectors 2i^+4j^−5k^2\hat{i}+4\hat{j}-5\hat{k} and…EasyNumerical value
  11. 9 Jan 2020, Shift 1 · Q75The projection of the line segment joining the points (1, −1-1, 3) and (2, −4-4, 11) on the line joining the points (−1-1, 2, 3) and (3,…EasyNumerical value

Shifts: 9 Jan 2020, Shift 1, 17 Mar 2021, Shift 2, 18 Mar 2021, Shift 2, 26 Aug 2021, Shift 2, 26 Jun 2022, Shift 2, 29 Jun 2022, Shift 1, 25 Jul 2022, Shift 2, 30 Jul 2022, Shift 2, 1 Feb 2024, Shift 2, 8 Apr 2024, Shift 2, 2 Apr 2025, Shift 1.

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