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Sunday, 25 October

JEE Main · Maths · Class 12

Vector Algebra: JEE Main previous year questions

142 questions in 101 of the 108 JEE Main shifts Lumi analysed, asked in 8 of 8 years. Here is what this chapter tests and how.

Study this chapter
Questions
142
in 101 of 108 shifts · 8 of 8 years
Average a shift
1.1
of 25 Maths · 1.2 since 2024 0.1
Typical range
0.9–1.6
questions a shift; fewest 0.9, most 1.7
Weighted estimate
1.1
model, recent years count more · about 4.6 marks
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

What to do

How to spend time on Vector Algebra

Priority

Should do

One of the 6 Maths chapters that took Maths from half to 80% of its questions in the 108 shifts analysed. How bands are set

Past questions
142in 101 of 108 shifts
Study plan gives it
20 hover 12 months; 15 h over 6
Study this chapter →

Ideas asked most often

  1. Solving Vector Equations with Cross Products20×
  2. Magnitude and Sine Formula13×
  3. Scalar and Vector Projection11×
  4. Lagrange's Identity8×
  5. Area of Triangles and Parallelograms7×

189 of the 255 ideas in Lumi’s map of this chapter have not been asked or touched in the shifts analysed. Of its idea-tagged questions from 2024 on, 15% tested an idea not asked in an earlier year, so learn the whole chapter, not just the list above.

Within each subject, chapters in NTA's 2026 syllabus are ranked by their average questions a shift over all 8 years analysed (history, not the model). Going down that list, the chapters that together held the first half of the subject's questions are Must do; the next ones, up to 80%, are Should do; the rest are Lower priority.

Key findings

Vector Algebra at a glance

  1. 01

    85%

    of its 48 questions from 2024 on that Lumi matched to an idea tested one JEE Main had asked in an earlier year; 100% came from a topic asked in an earlier year.

  2. 02

    74%

    of the 255 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    27%

    of its questions asked for a numerical answer, 0.9 times the Maths average.

  4. 04

    24%

    of its questions were rated hard, against 26% across all Maths questions in the same shifts.

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

0240.9’170.9’201’211’221.7’231.6’241’250.9’26

Raw count: 2017: 1 in 1 shift · 2020: 11 in 12 shifts · 2021: 29 in 24 shifts · 2022: 27 in 24 shifts · 2023: 24 in 12 shifts · 2024: 34 in 18 shifts · 2025: 8 in 8 shifts · 2026: 8 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step45%
  • Numerical answer27%
  • Calculation16%
  • Application9%
  • Two statements3%
  • Conceptual1%

Most common asks: unknown vector from cross and dot conditions (31); area of quadrilateral from vertices (3); unknown vector from dot product conditions (1).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Rank, all JEE chapters
#29
of 70 by weighted estimate
Rank in Maths
#10
of 21 chapters
Share of Maths
4.5%
of its questions, all shifts analysed
Busiest year
2023
1.7 questions a shift
Year to year
Some swing
varies by about 0.3 questions a shift
Long-run direction
+0.03
questions a shift, per year
Easy questions
12%
24% rated hard
Numerical answer
27%
0.9× the Maths rate
With a figure
0%
graph, diagram or structure
Study time
20 h
15 h on a 6-month plan
Marks per study hour
0.23
#49 of 70 chapters
Foundation for others
51%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 20171
  • 202011
  • 202129
  • 202227
  • 202324
  • 202434
  • 20258
  • 20268
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step64%
  • Calculation25%
  • Application9%
  • Conceptual2%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 255 ideas. In the 108 shifts analysed, JEE Main built a question around 44 of them. Most of the chapter has never been the main idea of a question, so past questions alone leave most of it out.

Asked as the main idea
44
Touched on in a question
22
Never asked
189

Topics

What repeats, topic by topic

This chapter's questions per topic in each year's analysed shifts. The number is the count; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. 5 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
022+questions in that year’s analysed shifts, shaded per shift
  • Cross Product

    As a topic: 72 questions in 8 of 8 years, most often single correct, 33% numerical answer. Recent asks: unknown vector from cross and dot conditions; numerical: solve vector cross product equation; numerical: area of triangle from vector combinations.

  • Dot Product

    As a topic: 36 questions in 7 of 8 years, most often single correct, 28% numerical answer.

  • Triple Products

    As a topic: 30 questions in 5 of 8 years, most often single correct, 20% numerical answer.

  • Linear Independence

    As a topic: 6 questions in 4 of 8 years, most often single correct.

Drill down

Topic, idea, question

Open a topic to see every idea JEE Main tested inside it, then open an idea to read the questions. Each row shows its 8 years.

  • Open71 · 50%31212122245

    13 ideas inside

    • OpenRepeated20 · 28%43273
    • OpenRepeated13 · 18%2323
    • OpenRepeated8 · 11%32
    • OpenRepeated7 · 10%5
    • OpenRepeated7 · 10%22
    • OpenRepeated6 · 8%2
    • OpenRepeated2 · 3%
    • OpenRepeated2 · 3%
    • OpenRepeated2 · 3%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
  • Open32 · 23%368932
  • Open28 · 20%59572
  • Open6 · 4%22

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

The exact ideas JEE Main has asked

Inside the topics, 42 different ideas were tested; 20 came more than once. These are the repeats, then the ideas new since 2024.

Dots are the 8 years with analysed shifts, 2017 to 2026.

Every question

All 142 Vector Algebra questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 20268 questions

  1. 2 Apr 2026, Shift 1 · Q14If a⃗\vec a and b⃗\vec b are two vectors such that ∣a⃗∣=2|\vec a|=2 and ∣b⃗∣=3|\vec b|=3, then the maximum value of…HardSingle correct
  2. 2 Apr 2026, Shift 2 · Q14Let the vectors a⃗=−i^+j^+3k^\vec{a} = -\hat{i} + \hat{j} + 3\hat{k} and b⃗=i^+3j^+k^\vec{b} = \hat{i} + 3\hat{j} + \hat{k}. For some…MediumSingle correct
  3. 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
  4. 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
  5. 5 Apr 2026, Shift 2 · Q16Let O be the origin, OP→=a⃗\overrightarrow{OP}=\vec{a} and OQ→=b⃗\overrightarrow{OQ}=\vec{b}. If R is the point on OP→\overrightarrow{OP} such that…EasySingle correct
  6. 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
  7. 6 Apr 2026, Shift 2 · Q15Let a⃗=2i^+3j^+3k^\vec{a}=2\hat{i}+3\hat{j}+3\hat{k} and b⃗=6i^+3j^+3k^\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}. Then the square of the area of the triangle with…EasySingle correct
  8. 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

JEE Main 20258 questions

  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. 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. 3 Apr 2025, Shift 1 · Q24Let a⃗=i^+j^+k^,b⃗=3i^+2j^−k^,c⃗=λj^+μk^\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = 3\hat{i} + 2\hat{j} - \hat{k}, \vec{c} = \lambda\hat{j} + \mu\hat{k} and d^\hat{d}…MediumNumerical value
  4. 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
  5. 4 Apr 2025, Shift 2 · Q24Let the three sides of a triangle ABC be given by the vectors 2i^−j^+k^2\hat{i}-\hat{j}+\hat{k}, i^−3j^−5k^\hat{i}-3\hat{j}-5\hat{k} and…MediumNumerical value
  6. 7 Apr 2025, Shift 1 · Q15Let the angle θ\theta, 0<θ<π20 < \theta < \frac{\pi}{2} between two unit vectors a^\hat{a} and b^\hat{b} be…MediumSingle correct
  7. 7 Apr 2025, Shift 2 · Q15Let a⃗\vec{a} and b⃗\vec{b} be the vectors of the same magnitude such that…MediumSingle correct
  8. 8 Apr 2025, Shift 2 · Q14Let a⃗=i^+2j^+k^\vec{a} = \hat{i} + 2\hat{j} + \hat{k} and b⃗=2i^+j^−k^\vec{b} = 2\hat{i} + \hat{j} - \hat{k}. Let c^\hat{c} be a unit vector in the plane of…MediumSingle correct

JEE Main 202434 questions

  1. 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
  2. 4 Apr 2024, Shift 1 · Q30Let ABC be a triangle of area 15215\sqrt{2} and the vectors AB→=i^+2j^−7k^\overrightarrow{AB}=\hat{i}+2\hat{j}-7\hat{k},…HardNumerical value
  3. 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
  4. 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
  5. 5 Apr 2024, Shift 1 · Q18If A(1,−1,2)A(1,-1,2), B(5,7,−6)B(5,7,-6), C(3,4,−10)C(3,4,-10) and D(−1,−4,−2)D(-1,-4,-2) are the vertices of a quadrilateral ABCD, then its area is :MediumSingle correct
  6. 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
  7. 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
  8. 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
  9. 6 Apr 2024, Shift 1 · Q19If A(3,1,−1)A(3,1,-1), B(53,73,13)B\left(\frac{5}{3},\frac{7}{3},\frac{1}{3}\right), C(2,2,1)C(2,2,1) and D(103,23,−13)D\left(\frac{10}{3},\frac{2}{3},\frac{-1}{3}\right)…MediumSingle correct
  10. 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
  11. 6 Apr 2024, Shift 2 · Q18Let a⃗=2i^+j^−k^\vec{a}=2\hat{i}+\hat{j}-\hat{k}, b⃗=((a⃗×(i^+j^))×i^)×i^\vec{b}=\left(\left(\vec{a}\times(\hat{i}+\hat{j})\right)\times\hat{i}\right)\times\hat{i}. Then…MediumSingle correct
  12. 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
  13. 8 Apr 2024, Shift 1 · Q18The set of all α\alpha, for which the vectors a⃗=αti^+6j^−3k^\vec{a}=\alpha t\hat{i}+6\hat{j}-3\hat{k} and…MediumSingle correct
  14. 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
  15. 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
  16. 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
  17. 9 Apr 2024, Shift 1 · Q17Let OA→=2a⃗\overrightarrow{OA}=2\vec{a}, OB→=6a⃗+5b⃗\overrightarrow{OB}=6\vec{a}+5\vec{b} and OC→=3b⃗\overrightarrow{OC}=3\vec{b}, where O is the origin. If…MediumSingle correct
  18. 9 Apr 2024, Shift 1 · Q18Let three vectors a⃗=αi^+4j^+2k^\vec{a}=\alpha\hat{i}+4\hat{j}+2\hat{k}, b⃗=5i^+3j^+4k^\vec{b}=5\hat{i}+3\hat{j}+4\hat{k}, c⃗=xi^+yj^+zk^\vec{c}=x\hat{i}+y\hat{j}+z\hat{k}…MediumSingle correct
  19. 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
  20. 9 Apr 2024, Shift 2 · Q18Let a⃗=2i^+αj^+k^, b⃗=−i^+k^, c⃗=βj^−k^\vec{a}=2\hat{i}+\alpha\hat{j}+\hat{k},\ \vec{b}=-\hat{i}+\hat{k},\ \vec{c}=\beta\hat{j}-\hat{k}, where α\alpha and β\beta are…MediumSingle correct
  21. 1 Feb 2024, Shift 1 · Q19Let a⃗=−5i^+j^−3k^\vec{a}=-5\hat{i}+\hat{j}-3\hat{k}, b⃗=i^+2j^−4k^\vec{b}=\hat{i}+2\hat{j}-4\hat{k} and…MediumSingle correct
  22. 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
  23. 1 Feb 2024, Shift 2 · Q30Let a⃗=i^+j^+k^\vec{a}=\hat{i}+\hat{j}+\hat{k}, b⃗=−i^−8j^+2k^\vec{b}=-\hat{i}-8\hat{j}+2\hat{k} and c⃗=4i^+c2j^+c3k^\vec{c}=4\hat{i}+c_2\hat{j}+c_3\hat{k} be three vectors…MediumNumerical value
  24. 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
  25. 27 Jan 2024, Shift 1 · Q28Acute and Obtuse Angle Conditions · Easy · Numerical value
  26. 29 Jan 2024, Shift 1 · Q17Linear Combination Concept · Medium · Single correct
  27. 29 Jan 2024, Shift 1 · Q18Angle Bisector Construction · Medium · Single correct
  28. 30 Jan 2024, Shift 1 · Q17Area of Quadrilateral via Diagonals · Medium · Single correct
  29. 30 Jan 2024, Shift 1 · Q18Magnitude and Sine Formula · Hard · Single correct
  30. 30 Jan 2024, Shift 2 · Q18Expansion of Sum of Vectors Squared · Easy · Single correct
  31. 30 Jan 2024, Shift 2 · Q19Lagrange's Identity · Medium · Single correct
  32. 31 Jan 2024, Shift 1 · Q18Solving Vector Equations with Cross Products · Medium · Single correct
  33. 31 Jan 2024, Shift 1 · Q30Lagrange's Identity · Medium · Numerical value
  34. 31 Jan 2024, Shift 2 · Q30Solving Vector Equations with Cross Products · Hard · Numerical value

JEE Main 202324 questions

  1. 6 Apr 2023, Shift 1 · Q15Coplanarity of Four Points · Medium · Single correct
  2. 6 Apr 2023, Shift 1 · Q16Lagrange's Identity · Medium · Single correct
  3. 6 Apr 2023, Shift 2 · Q17Coplanarity of Four Points · Medium · Single correct
  4. 6 Apr 2023, Shift 2 · Q18STP Geometric Interpretation · Medium · Single correct
  5. 8 Apr 2023, Shift 1 · Q17Collinearity of Three Position Vectors · Medium · Single correct
  6. 8 Apr 2023, Shift 1 · Q29Solving Vector Equations with Cross Products · Hard · Numerical value
  7. 8 Apr 2023, Shift 2 · Q15Area of Quadrilateral via Diagonals · Medium · Single correct
  8. 8 Apr 2023, Shift 2 · Q16Parametric Coplanarity via STP · Hard · Single correct
  9. 10 Apr 2023, Shift 1 · Q16Determinant Calculation Method · Medium · Single correct
  10. 10 Apr 2023, Shift 1 · Q17Unique Linear Combinations · Medium · Single correct
  11. 10 Apr 2023, Shift 2 · Q16Unit Normal Vector Calculation · Medium · Single correct
  12. 10 Apr 2023, Shift 2 · Q17Orthocenter Position Vector Relations · Medium · Single correct
  13. 11 Apr 2023, Shift 1 · Q11Magnitude and Sine Formula · Hard · Single correct
  14. 11 Apr 2023, Shift 1 · Q12Open the question · Medium · Two statements
  15. 11 Apr 2023, Shift 2 · Q17Coplanarity of Four Points · Medium · Single correct
  16. 11 Apr 2023, Shift 2 · Q29Magnitude and Sine Formula · Hard · Numerical value
  17. 12 Apr 2023, Shift 1 · Q16Solving for Unknown in Coplanarity · Medium · Single correct
  18. 12 Apr 2023, Shift 1 · Q17Condition for Parallel Vectors · Hard · Single correct
  19. 13 Apr 2023, Shift 1 · Q9Simultaneous Cross and Dot Equations · Medium · Single correct
  20. 13 Apr 2023, Shift 1 · Q28Solving Vector Equations with Cross Products · Medium · Numerical value
  21. 13 Apr 2023, Shift 2 · Q17Anti-commutativity and Distributivity · Medium · Single correct
  22. 13 Apr 2023, Shift 2 · Q18Area of Triangles and Parallelograms · Medium · Single correct
  23. 15 Apr 2023, Shift 1 · Q16Solving for Unknown in Coplanarity · Medium · Single correct
  24. 15 Apr 2023, Shift 1 · Q17Open the question · Easy · Single correct

JEE Main 202227 questions

  1. 25 Jul 2022, Shift 1 · Q15Magnitude and Sine Formula · Hard · Two statements
  2. 25 Jul 2022, Shift 2 · Q17Scalar and Vector Projection · Medium · Single correct
  3. 26 Jul 2022, Shift 1 · Q15Magnitude and Sine Formula · Medium · Single correct
  4. 27 Jul 2022, Shift 1 · Q13VTP BAC-CAB Expansion · Medium · Single correct
  5. 28 Jul 2022, Shift 1 · Q3Independence of Three Vectors · Easy · Single correct
  6. 28 Jul 2022, Shift 1 · Q6Orthogonality Condition · Medium · Single correct
  7. 28 Jul 2022, Shift 2 · Q77Acute and Obtuse Angle Conditions · Medium · Single correct
  8. 29 Jul 2022, Shift 1 · Q10VTP BAC-CAB Expansion · Medium · Single correct
  9. 29 Jul 2022, Shift 1 · Q14Magnitude and Sine Formula · Hard · Single correct
  10. 29 Jul 2022, Shift 2 · Q18Lagrange's Identity · Hard · Single correct
  11. 29 Jul 2022, Shift 2 · Q29Lagrange's Identity · Medium · Numerical value
  12. 30 Jul 2022, Shift 2 · Q88Scalar and Vector Projection · Hard · Numerical value
  13. 24 Jun 2022, Shift 1 · Q16Solving Vector Equations with Cross Products · Hard · Single correct
  14. 24 Jun 2022, Shift 2 · Q16Lagrange's Identity (Dot Product Form) · Hard · Two statements
  15. 25 Jun 2022, Shift 1 · Q14Vectors with Equal Inclination · Hard · Single correct
  16. 25 Jun 2022, Shift 1 · Q23Lagrange's Identity · Medium · Numerical value
  17. 25 Jun 2022, Shift 2 · Q26Simultaneous Cross and Dot Equations · Hard · Numerical value
  18. 26 Jun 2022, Shift 1 · Q16VTP BAC-CAB Expansion · Medium · Single correct
  19. 26 Jun 2022, Shift 2 · Q16Scalar and Vector Projection · Medium · Single correct
  20. 27 Jun 2022, Shift 1 · Q15Solving Vector Equations with Cross Products · Medium · Single correct
  21. 27 Jun 2022, Shift 2 · Q15Area of Quadrilateral via Diagonals · Hard · Single correct
  22. 28 Jun 2022, Shift 1 · Q24Solving for Unknown in Coplanarity · Medium · Numerical value
  23. 28 Jun 2022, Shift 2 · Q14Area of Triangles and Parallelograms · Medium · Single correct
  24. 28 Jun 2022, Shift 2 · Q19Solving Vector Equations with Cross Products · Hard · Single correct
  25. 29 Jun 2022, Shift 1 · Q5Scalar and Vector Projection · Medium · Single correct
  26. 29 Jun 2022, Shift 2 · Q15Collinearity of Three Position Vectors · Easy · Single correct
  27. 30 Jun 2022, Shift 1 · Q17Solving for Unknown in Coplanarity · Hard · Single correct

JEE Main 202129 questions

  1. 3 Aug 2021, Shift 2 · Q90Determinant Calculation Method · Medium · Numerical value
  2. 4 Aug 2021, Shift 1 · Q76Open the question · Easy · Single correct
  3. 4 Aug 2021, Shift 2 · Q85Simultaneous Cross and Dot Equations · Medium · Numerical value
  4. 26 Aug 2021, Shift 1 · Q77Solving Vector Equations with Cross Products · Medium · Single correct
  5. 26 Aug 2021, Shift 2 · Q87Scalar and Vector Projection · Easy · Numerical value
  6. 27 Aug 2021, Shift 1 · Q89Magnitude and Sine Formula · Medium · Numerical value
  7. 31 Aug 2021, Shift 1 · Q78Expansion of Sum of Vectors Squared · Medium · Single correct
  8. 31 Aug 2021, Shift 2 · Q75VTP BAC-CAB Expansion · Hard · Single correct
  9. 24 Feb 2021, Shift 1 · Q89Constructing Orthogonal Coplanar Vectors · Medium · Numerical value
  10. 25 Feb 2021, Shift 1 · Q90Solving Vector Equations with Cross Products · Medium · Numerical value
  11. 25 Feb 2021, Shift 2 · Q90Area of Triangles and Parallelograms · Easy · Numerical value
  12. 26 Feb 2021, Shift 1 · Q61VTP with Repeated Vectors · Easy · Single correct
  13. 26 Feb 2021, Shift 2 · Q71Proportionality Test for Collinearity · Easy · Single correct
  14. 22 Jul 2021, Shift 2 · Q72Orthogonal Triad Expansion · Medium · Single correct
  15. 22 Jul 2021, Shift 2 · Q80STP Algebraic Properties · Hard · Single correct
  16. 25 Jul 2021, Shift 1 · Q71Solving for Unknown in Coplanarity · Medium · Single correct
  17. 25 Jul 2021, Shift 1 · Q82Unit Normal Vector Calculation · Easy · Numerical value
  18. 25 Jul 2021, Shift 2 · Q78Lagrange's Identity · Easy · Single correct
  19. 25 Jul 2021, Shift 2 · Q80Solving for Unknown in Coplanarity · Medium · Single correct
  20. 25 Jul 2021, Shift 2 · Q88Angle Between Vectors · Medium · Numerical value
  21. 16 Mar 2021, Shift 2 · Q63Solving Vector Equations with Cross Products · Hard · Single correct
  22. 16 Mar 2021, Shift 2 · Q84STP Definition and Determinant · Medium · Numerical value
  23. 17 Mar 2021, Shift 1 · Q78Solving Vector Equations with Cross Products · Medium · Single correct
  24. 17 Mar 2021, Shift 1 · Q90STP Definition and Determinant · Medium · Numerical value
  25. 17 Mar 2021, Shift 2 · Q63STP Definition and Determinant · Medium · Single correct
  26. 17 Mar 2021, Shift 2 · Q89Scalar and Vector Projection · Hard · Numerical value
  27. 18 Mar 2021, Shift 1 · Q80Dot Product Invariance Under Rotation · Medium · Single correct
  28. 18 Mar 2021, Shift 2 · Q66Scalar and Vector Projection · Medium · Single correct
  29. 18 Mar 2021, Shift 2 · Q80Magnitude and Sine Formula · Medium · Single correct

JEE Main 202011 questions

  1. 8 Jan 2020, Shift 1 · Q66STP Geometric Interpretation · Medium · Single correct
  2. 8 Jan 2020, Shift 2 · Q67Solving Vector Equations with Cross Products · Medium · Single correct
  3. 9 Jan 2020, Shift 1 · Q73Solving for Unknown in Coplanarity · Medium · Numerical value
  4. 9 Jan 2020, Shift 2 · Q75Magnitude and Sine Formula · Medium · Numerical value
  5. 2 Sep 2020, Shift 1 · Q75Algebraic Properties · Easy · Numerical value
  6. 2 Sep 2020, Shift 2 · Q73Lagrange's Identity · Medium · Numerical value
  7. 3 Sep 2020, Shift 2 · Q69Angle Between Vectors · Hard · Single correct
  8. 4 Sep 2020, Shift 1 · Q67STP Definition and Determinant · Medium · Single correct
  9. 4 Sep 2020, Shift 2 · Q75Perpendicular Vector Component via VTP · Medium · Numerical value
  10. 5 Sep 2020, Shift 1 · Q67STP Geometric Interpretation · Medium · Single correct
  11. 6 Sep 2020, Shift 2 · Q74Expansion of Sum of Vectors Squared · Easy · Numerical value

JEE Main 20171 question

  1. 2 Apr 2017 (offline) · Q84Magnitude and Sine Formula · Hard · Single correct

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

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