Skip to main content
ExamCompass
Exam Compass LogoExamCompass
BlogFounderAppLogin

Exams

JEE Main & AdvancedNEET UGClass 12 BoardsClass 11 Boards

Categories

All ArticlesExam NotesRevision
Meet the FounderDownload Android & iOS AppLogin
Home/JEE MAINS/mathematics/vector algebra
Curated PYQ Collection

Top 50 Most Repeated VECTOR ALGEBRA PYQs | JEE MAINS

A curated collection of the most important questions from VECTOR ALGEBRA, fully solved with step-by-step concepts to prepare for JEE MAINS.

Question #1

Practice Question

A.$5\sqrt{3}$
B.$\sqrt{75}$
C.$\sqrt{14}$
D.$7\sqrt{3}$

Concept Applied

The area equals the magnitude of the cross product $|\mathbf{a}\times\mathbf{b}|$. Computing $\mathbf{a}\times\mathbf{b}= -\hat{i}-5\hat{j}-7\hat{k}$,...

Read Full Step-by-Step Solution →

Question #2

Practice Question

Concept Applied

Magnitude is $\sqrt{2^2+3^2+6^2} = 7$....

Read Full Step-by-Step Solution →

Question #3

Practice Question

Concept Applied

Vectors are perpendicular, so magnitude is $\sqrt{3^2+4^2}=5$....

Read Full Step-by-Step Solution →

Question #4

Practice Question

Concept Applied

Cross product magnitude equals area of parallelogram formed by vectors....

Read Full Step-by-Step Solution →

Question #5

Practice Question

Concept Applied

Coplanar vectors have scalar triple product zero. Solve $[\vec{a}\ \vec{b}\ \vec{c}] = 0$ to get $\lambda + \mu = 5$....

Read Full Step-by-Step Solution →

Question #6

Practice Question

A.30°
B.45°
C.64°
D.90°

Concept Applied

Compute $\vec{A}\cdot\vec{B}=3\times5+4\times(-1)=11$. Magnitudes: $|\vec{A}|=5$, $|\vec{B}|=\sqrt{26}\approx5.099$. Then $\cos\theta=\frac{11}{5\time...

Read Full Step-by-Step Solution →

Question #7

Practice Question

A.$\vec{r} = \vec{a} + t\vec{b}$
B.$\vec{r} = t\vec{a} + \vec{b}$
C.$\vec{r} \cdot \vec{b} = 0$
D.$\vec{r} = \vec{a} \times \vec{b}$

Concept Applied

Standard vector form: point + scalar × direction vector....

Read Full Step-by-Step Solution →

Question #8

Practice Question

Concept Applied

Volume = absolute value of scalar triple product....

Read Full Step-by-Step Solution →

Question #9

Practice Question

A.$\vec{r} = 2\hat{i} + \hat{j} + \lambda(3\hat{i} - \hat{k})$
B.$\vec{r} = 3\hat{i} - \hat{k} + \lambda(2\hat{i} + \hat{j})$
C.$\vec{r} = \lambda(3\hat{i} - \hat{k})$
D.$\vec{r} = (2\hat{i} + \hat{j}) + \lambda(\hat{i} + \hat{j})$

Concept Applied

Line: $\vec{r} = \vec{a} + \lambda\vec{b}$; use given point and direction vector....

Read Full Step-by-Step Solution →

Question #10

Practice Question

A.$5\sqrt{3}$
B.$\sqrt{75}$
C.$\sqrt{14}$
D.$7\sqrt{3}$

Concept Applied

The area equals the magnitude of the cross product $|\mathbf{a}\times\mathbf{b}|$. Computing $\mathbf{a}\times\mathbf{b}= -\hat{i}-5\hat{j}-7\hat{k}$,...

Read Full Step-by-Step Solution →

Question #11

Practice Question

Concept Applied

Magnitude is $\sqrt{2^2+3^2+6^2} = 7$....

Read Full Step-by-Step Solution →

Question #12

Practice Question

Concept Applied

Vectors are perpendicular, so magnitude is $\sqrt{3^2+4^2}=5$....

Read Full Step-by-Step Solution →

Question #13

Practice Question

Concept Applied

Cross product magnitude equals area of parallelogram formed by vectors....

Read Full Step-by-Step Solution →

Question #14

Practice Question

Concept Applied

Coplanar vectors have scalar triple product zero. Solve $[\vec{a}\ \vec{b}\ \vec{c}] = 0$ to get $\lambda + \mu = 5$....

Read Full Step-by-Step Solution →

Question #15

Practice Question

A.30°
B.45°
C.64°
D.90°

Concept Applied

Compute $\vec{A}\cdot\vec{B}=3\times5+4\times(-1)=11$. Magnitudes: $|\vec{A}|=5$, $|\vec{B}|=\sqrt{26}\approx5.099$. Then $\cos\theta=\frac{11}{5\time...

Read Full Step-by-Step Solution →

Question #16

Practice Question

A.$\vec{r} = \vec{a} + t\vec{b}$
B.$\vec{r} = t\vec{a} + \vec{b}$
C.$\vec{r} \cdot \vec{b} = 0$
D.$\vec{r} = \vec{a} \times \vec{b}$

Concept Applied

Standard vector form: point + scalar × direction vector....

Read Full Step-by-Step Solution →

Question #17

Practice Question

Concept Applied

Volume = absolute value of scalar triple product....

Read Full Step-by-Step Solution →

Question #18

Practice Question

A.$\vec{r} = 2\hat{i} + \hat{j} + \lambda(3\hat{i} - \hat{k})$
B.$\vec{r} = 3\hat{i} - \hat{k} + \lambda(2\hat{i} + \hat{j})$
C.$\vec{r} = \lambda(3\hat{i} - \hat{k})$
D.$\vec{r} = (2\hat{i} + \hat{j}) + \lambda(\hat{i} + \hat{j})$

Concept Applied

Line: $\vec{r} = \vec{a} + \lambda\vec{b}$; use given point and direction vector....

Read Full Step-by-Step Solution →

Question #19

Practice Question

A.$5\sqrt{3}$
B.$\sqrt{75}$
C.$\sqrt{14}$
D.$7\sqrt{3}$

Concept Applied

The area equals the magnitude of the cross product $|\mathbf{a}\times\mathbf{b}|$. Computing $\mathbf{a}\times\mathbf{b}= -\hat{i}-5\hat{j}-7\hat{k}$,...

Read Full Step-by-Step Solution →

Question #20

Practice Question

Concept Applied

Magnitude is $\sqrt{2^2+3^2+6^2} = 7$....

Read Full Step-by-Step Solution →

Question #21

Practice Question

Concept Applied

Vectors are perpendicular, so magnitude is $\sqrt{3^2+4^2}=5$....

Read Full Step-by-Step Solution →

Question #22

Practice Question

Concept Applied

Cross product magnitude equals area of parallelogram formed by vectors....

Read Full Step-by-Step Solution →

Question #23

Practice Question

Concept Applied

Coplanar vectors have scalar triple product zero. Solve $[\vec{a}\ \vec{b}\ \vec{c}] = 0$ to get $\lambda + \mu = 5$....

Read Full Step-by-Step Solution →

Question #24

Practice Question

A.30°
B.45°
C.64°
D.90°

Concept Applied

Compute $\vec{A}\cdot\vec{B}=3\times5+4\times(-1)=11$. Magnitudes: $|\vec{A}|=5$, $|\vec{B}|=\sqrt{26}\approx5.099$. Then $\cos\theta=\frac{11}{5\time...

Read Full Step-by-Step Solution →

Question #25

Practice Question

A.$\vec{r} = \vec{a} + t\vec{b}$
B.$\vec{r} = t\vec{a} + \vec{b}$
C.$\vec{r} \cdot \vec{b} = 0$
D.$\vec{r} = \vec{a} \times \vec{b}$

Concept Applied

Standard vector form: point + scalar × direction vector....

Read Full Step-by-Step Solution →

Question #26

Practice Question

Concept Applied

Volume = absolute value of scalar triple product....

Read Full Step-by-Step Solution →

Question #27

Practice Question

A.$\vec{r} = 2\hat{i} + \hat{j} + \lambda(3\hat{i} - \hat{k})$
B.$\vec{r} = 3\hat{i} - \hat{k} + \lambda(2\hat{i} + \hat{j})$
C.$\vec{r} = \lambda(3\hat{i} - \hat{k})$
D.$\vec{r} = (2\hat{i} + \hat{j}) + \lambda(\hat{i} + \hat{j})$

Concept Applied

Line: $\vec{r} = \vec{a} + \lambda\vec{b}$; use given point and direction vector....

Read Full Step-by-Step Solution →

Question #28

Practice Question

A.$5\sqrt{3}$
B.$\sqrt{75}$
C.$\sqrt{14}$
D.$7\sqrt{3}$

Concept Applied

The area equals the magnitude of the cross product $|\mathbf{a}\times\mathbf{b}|$. Computing $\mathbf{a}\times\mathbf{b}= -\hat{i}-5\hat{j}-7\hat{k}$,...

Read Full Step-by-Step Solution →

Question #29

Practice Question

Concept Applied

Magnitude is $\sqrt{2^2+3^2+6^2} = 7$....

Read Full Step-by-Step Solution →

Question #30

Practice Question

Concept Applied

Vectors are perpendicular, so magnitude is $\sqrt{3^2+4^2}=5$....

Read Full Step-by-Step Solution →

Question #31

Practice Question

Concept Applied

Cross product magnitude equals area of parallelogram formed by vectors....

Read Full Step-by-Step Solution →

Question #32

Practice Question

Concept Applied

Coplanar vectors have scalar triple product zero. Solve $[\vec{a}\ \vec{b}\ \vec{c}] = 0$ to get $\lambda + \mu = 5$....

Read Full Step-by-Step Solution →

Question #33

Practice Question

A.30°
B.45°
C.64°
D.90°

Concept Applied

Compute $\vec{A}\cdot\vec{B}=3\times5+4\times(-1)=11$. Magnitudes: $|\vec{A}|=5$, $|\vec{B}|=\sqrt{26}\approx5.099$. Then $\cos\theta=\frac{11}{5\time...

Read Full Step-by-Step Solution →

Question #34

Practice Question

A.$\vec{r} = \vec{a} + t\vec{b}$
B.$\vec{r} = t\vec{a} + \vec{b}$
C.$\vec{r} \cdot \vec{b} = 0$
D.$\vec{r} = \vec{a} \times \vec{b}$

Concept Applied

Standard vector form: point + scalar × direction vector....

Read Full Step-by-Step Solution →

Question #35

Practice Question

Concept Applied

Volume = absolute value of scalar triple product....

Read Full Step-by-Step Solution →

Question #36

Practice Question

A.$\vec{r} = 2\hat{i} + \hat{j} + \lambda(3\hat{i} - \hat{k})$
B.$\vec{r} = 3\hat{i} - \hat{k} + \lambda(2\hat{i} + \hat{j})$
C.$\vec{r} = \lambda(3\hat{i} - \hat{k})$
D.$\vec{r} = (2\hat{i} + \hat{j}) + \lambda(\hat{i} + \hat{j})$

Concept Applied

Line: $\vec{r} = \vec{a} + \lambda\vec{b}$; use given point and direction vector....

Read Full Step-by-Step Solution →

Question #37

Practice Question

A.$5\sqrt{3}$
B.$\sqrt{75}$
C.$\sqrt{14}$
D.$7\sqrt{3}$

Concept Applied

The area equals the magnitude of the cross product $|\mathbf{a}\times\mathbf{b}|$. Computing $\mathbf{a}\times\mathbf{b}= -\hat{i}-5\hat{j}-7\hat{k}$,...

Read Full Step-by-Step Solution →

Question #38

Practice Question

Concept Applied

Magnitude is $\sqrt{2^2+3^2+6^2} = 7$....

Read Full Step-by-Step Solution →

Question #39

Practice Question

Concept Applied

Vectors are perpendicular, so magnitude is $\sqrt{3^2+4^2}=5$....

Read Full Step-by-Step Solution →

Question #40

Practice Question

Concept Applied

Cross product magnitude equals area of parallelogram formed by vectors....

Read Full Step-by-Step Solution →

Question #41

Practice Question

Concept Applied

Coplanar vectors have scalar triple product zero. Solve $[\vec{a}\ \vec{b}\ \vec{c}] = 0$ to get $\lambda + \mu = 5$....

Read Full Step-by-Step Solution →

Question #42

Practice Question

A.30°
B.45°
C.64°
D.90°

Concept Applied

Compute $\vec{A}\cdot\vec{B}=3\times5+4\times(-1)=11$. Magnitudes: $|\vec{A}|=5$, $|\vec{B}|=\sqrt{26}\approx5.099$. Then $\cos\theta=\frac{11}{5\time...

Read Full Step-by-Step Solution →

Question #43

Practice Question

A.$\vec{r} = \vec{a} + t\vec{b}$
B.$\vec{r} = t\vec{a} + \vec{b}$
C.$\vec{r} \cdot \vec{b} = 0$
D.$\vec{r} = \vec{a} \times \vec{b}$

Concept Applied

Standard vector form: point + scalar × direction vector....

Read Full Step-by-Step Solution →

Question #44

Practice Question

Concept Applied

Volume = absolute value of scalar triple product....

Read Full Step-by-Step Solution →

Question #45

Practice Question

A.$\vec{r} = 2\hat{i} + \hat{j} + \lambda(3\hat{i} - \hat{k})$
B.$\vec{r} = 3\hat{i} - \hat{k} + \lambda(2\hat{i} + \hat{j})$
C.$\vec{r} = \lambda(3\hat{i} - \hat{k})$
D.$\vec{r} = (2\hat{i} + \hat{j}) + \lambda(\hat{i} + \hat{j})$

Concept Applied

Line: $\vec{r} = \vec{a} + \lambda\vec{b}$; use given point and direction vector....

Read Full Step-by-Step Solution →

Question #46

Practice Question

A.$5\sqrt{3}$
B.$\sqrt{75}$
C.$\sqrt{14}$
D.$7\sqrt{3}$

Concept Applied

The area equals the magnitude of the cross product $|\mathbf{a}\times\mathbf{b}|$. Computing $\mathbf{a}\times\mathbf{b}= -\hat{i}-5\hat{j}-7\hat{k}$,...

Read Full Step-by-Step Solution →

Question #47

Practice Question

Concept Applied

Magnitude is $\sqrt{2^2+3^2+6^2} = 7$....

Read Full Step-by-Step Solution →

Question #48

Practice Question

Concept Applied

Vectors are perpendicular, so magnitude is $\sqrt{3^2+4^2}=5$....

Read Full Step-by-Step Solution →

Question #49

Practice Question

Concept Applied

Cross product magnitude equals area of parallelogram formed by vectors....

Read Full Step-by-Step Solution →

Question #50

Practice Question

Concept Applied

Coplanar vectors have scalar triple product zero. Solve $[\vec{a}\ \vec{b}\ \vec{c}] = 0$ to get $\lambda + \mu = 5$....

Read Full Step-by-Step Solution →
ExamCompass

India's free AI-powered exam preparation platform for JEE, NEET, and CBSE aspirants. 9,000+ verified PYQs.

Competitive Exams

  • JEE Mains 2026
  • JEE Advanced 2026
  • NEET UG 2026

Board Exams

  • Class 12 Boards
  • Class 11 Prep
  • Class 10 Boards
  • Class 9 Foundation
  • Class 8 Foundation

Resources

  • Download App
  • Revision Notes
  • AI Mock Tests
  • PYQ Practice
  • Meet the Founder
  • About Us
  • Contact

Legal

  • Privacy Policy
  • Terms of Service

Exam Compass is India's free AI-powered exam preparation platform. Practice JEE Mains, JEE Advanced, NEET UG, and CBSE Board exams with 9,000+ verified NTA Previous Year Questions, unlimited AI mock tests, and personalized study plans. All free, forever.

© 2026 Exam Compass. All rights reserved.

Built with ❤️ in India by Ayush Kumar