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Saturday, 10 October

JEE Main Maths · Class 12

Vector Algebra: JEE Main previous year questions

Vector Algebra had 55 questions in the 42 JEE Main shifts Lumi analysed, about 1.2 a shift, asked in 41 of 42 shifts. It ranks 9 of 22 Maths chapters by questions; 22% of its questions were hard.

Questions
55
in 41 of 42 shifts
A shift, on average
1.2
of 25 Maths questions
Since 2024
-0.0
1.2 a shift in 2017–23, 1.2 in 2024–26
Numerical answer
13
24% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
08161’174’206’215’228’2315’248’258’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20204
  • 20216
  • 20225
  • 20238
  • 202415
  • 20258
  • 20268
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

4 topics and 29 distinct ideas; 8 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

3 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
8 repeat

Study it on Lumi

Vector Algebra: the interactive lesson

Every question

All 55 Vector Algebra questions

Newest first. Each opens with its options and the official answer.

2026 8 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

2025 8 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

2024 15 questions

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  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. 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
  9. 29 Jan 2024, Shift 1 · Q17Let a⃗,b⃗\vec{a},\vec{b} and c⃗\vec{c} be three non-zero vectors such that b⃗\vec{b} and c⃗\vec{c} are non-collinear. If a⃗+5b⃗\vec{a}+5\vec{b}…MediumSingle correct
  10. 29 Jan 2024, Shift 1 · Q18Let O be the origin and the position vectors of A and B be 2i^+2j^+k^2\hat{i}+2\hat{j}+\hat{k} and 2i^+4j^+4k^2\hat{i}+4\hat{j}+4\hat{k} respectively. If…MediumSingle correct
  11. 30 Jan 2024, Shift 2 · Q18Let a⃗\vec{a} and b⃗\vec{b} be two vectors such that ∣b⃗∣=1|\vec{b}| = 1 and ∣b⃗×a⃗∣=2|\vec{b} \times \vec{a}| = 2. Then…EasySingle correct
  12. 30 Jan 2024, Shift 2 · Q19Let a⃗=i^+αj^+βk^\vec{a} = \hat{i} + \alpha\hat{j} + \beta\hat{k}, α,β∈R\alpha, \beta \in \mathbb{R}. Let a vector b⃗\vec{b} be such that the angle…MediumSingle correct
  13. 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
  14. 31 Jan 2024, Shift 1 · Q30Let a⃗\vec{a} and b⃗\vec{b} be two vectors such that ∣a⃗∣=1, ∣b⃗∣=4|\vec{a}|=1,\ |\vec{b}|=4, and a⃗⋅b⃗=2\vec{a}\cdot\vec{b}=2. If…MediumNumerical value
  15. 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

2023 8 questions

  1. 6 Apr 2023, Shift 1 · Q15Let the position vectors of the points A, B, C and D be 5i^+5j^+2λk^5\hat i+5\hat j+2\lambda\hat k, i^+2j^+3k^\hat i+2\hat j+3\hat k,…MediumSingle correct
  2. 6 Apr 2023, Shift 1 · Q16Let a⃗=2i^+3j^+4k^\vec a=2\hat i+3\hat j+4\hat k, b⃗=i^−2j^−2k^\vec b=\hat i-2\hat j-2\hat k and c⃗=−i^+4j^+3k^\vec c=-\hat i+4\hat j+3\hat k. If d⃗\vec d is a vector…MediumSingle correct
  3. 8 Apr 2023, Shift 2 · Q15The area of the quadrilateral ABCDABCD with vertices A(2,1,1)A(2, 1, 1), B(1,2,5)B(1, 2, 5), C(−2,−3,5)C(-2, -3, 5) and D(1,−6,−7)D(1, -6, -7) is equal toMediumSingle correct
  4. 8 Apr 2023, Shift 2 · Q16Let the vectors u⃗1=i^+j^+ak^\vec{u}_1 = \hat{i} + \hat{j} + a\hat{k}, u⃗2=i^+bj^+k^\vec{u}_2 = \hat{i} + b\hat{j} + \hat{k} and…HardSingle correct
  5. 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
  6. 11 Apr 2023, Shift 1 · Q12For any vector a⃗=a1i^+a2j^+a3k^\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}, with 10∣ai∣<1, i=1,2,310|a_i| < 1,\ i = 1, 2, 3, consider the following statements : (A)…MediumTwo statements
  7. 13 Apr 2023, Shift 2 · Q17Let ∣a⃗∣=2|\vec{a}|=2, ∣b⃗∣=3|\vec{b}|=3 and the angle between the vectors a⃗\vec{a} and b⃗\vec{b} be π4\frac{\pi}{4}. Then…MediumSingle correct
  8. 13 Apr 2023, Shift 2 · Q18Let for a triangle ABC, AB→=−2i^+j^+3k^\overrightarrow{AB}=-2\hat{i}+\hat{j}+3\hat{k} CB→=αi^+βj^+γk^\overrightarrow{CB}=\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}…MediumSingle correct

2022 5 questions

  1. 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
  2. 28 Jul 2022, Shift 1 · Q3Let the vectors a⃗=(1+t)i^+(1−t)j^+k^, b⃗=(1−t)i^+(1+t)j^+2k^\vec{a}=(1+t)\hat{i}+(1-t)\hat{j}+\hat{k},\ \vec{b}=(1-t)\hat{i}+(1+t)\hat{j}+2\hat{k} and…EasySingle correct
  3. 28 Jul 2022, Shift 1 · Q6Let a vector a⃗\vec{a} has magnitude 9. Let a vector b⃗\vec{b} be such that for every (x,y)∈R×R−{(0,0)}(x,y)\in\mathbf{R}\times\mathbf{R}-\{(0,0)\}, the…MediumSingle correct
  4. 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
  5. 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

2021 6 questions

  1. 3 Aug 2021, Shift 2 · Q90Let a⃗=2i^+αj^+k^\vec{a} = 2\hat{i} + \alpha\hat{j} + \hat{k} and b⃗=βi^−5j^+γk^\vec{b} = \beta\hat{i} - 5\hat{j} + \gamma\hat{k}, where α\alpha, β\beta and…MediumNumerical value
  2. 25 Jul 2021, Shift 1 · Q71Let the vectors (2+a+b)i^+(a+2b+c)j^−(b+c)k^(2+a+b)\hat{i}+(a+2b+c)\hat{j}-(b+c)\hat{k}, (1+b)i^+2bj^−bk^(1+b)\hat{i}+2b\hat{j}-b\hat{k} and…MediumSingle correct
  3. 25 Jul 2021, Shift 1 · Q82Let p⃗=2i^+3j^+k^\vec{p}=2\hat{i}+3\hat{j}+\hat{k} and q⃗=i^+2j^+k^\vec{q}=\hat{i}+2\hat{j}+\hat{k} be two vectors. If a vector…EasyNumerical value
  4. 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
  5. 16 Mar 2021, Shift 2 · Q84Let c⃗\vec c be a vector perpendicular to the vectors a⃗=i^+j^−k^\vec a=\hat i+\hat j-\hat k and b⃗=i^+2j^+k^\vec b=\hat i+2\hat j+\hat k. If…MediumNumerical value
  6. 18 Mar 2021, Shift 1 · Q80A vector a⃗\vec{a} has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle…MediumSingle correct

2020 4 questions

  1. 8 Jan 2020, Shift 1 · Q66Let the volume of a parallelopiped whose coterminous edges are given by u⃗=i^+j^+λk^\vec{u}=\hat{i}+\hat{j}+\lambda\hat{k},…MediumSingle correct
  2. 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
  3. 2 Sep 2020, Shift 1 · Q75Let a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} be three unit vectors such that ∣a⃗−b⃗∣2+∣a⃗−c⃗∣2=8|\vec{a}-\vec{b}|^{2}+|\vec{a}-\vec{c}|^{2}=8. Then…EasyNumerical value
  4. 6 Sep 2020, Shift 2 · Q74If x⃗\vec{x} and y⃗\vec{y} be two non-zero vectors such that ∣x⃗+y⃗∣=∣x⃗∣|\vec{x}+\vec{y}|=|\vec{x}| and 2x⃗+λy⃗2\vec{x}+\lambda\vec{y} is perpendicular…EasyNumerical value

2017 1 questions

  1. 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

Pattern: Asked most years.