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JEE Main - Vector Algebra Notes (Free PDF Download)

Last updated date: 20th Jul 2024
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Study Smart with JEE Main - Vector Algebra Notes and Important Topics

Get ready for your JEE Main exam by getting hold of important Vector Algebra Notes. Our expert teachers create these notes to make tough concepts easy, highlight important stuff, and cover important topics. You can get them for FREE from our website. These notes give you all the important info you need in a simpler way, helping you study better. You'll understand the subjects well and be well-prepared for the exam after reviewing these notes. Use these helpful resources to do great in JEE Main.


JEE Main Revision Notes


Text, Images, Videos and PDF


JEE Main

Chapter Name:

Vector Algebra

Academic Session:



English Medium



Available Material:

Chapter-wise Notes with PDF

The  Vector Algebra chapter covers the study of vectors, which are mathematical quantities with both magnitude and direction. This is one of the important chapters for JEE Main Exams, and you can expect a minimum of 2 to3 questions from this chapter. Have a look at the number of questions asked from the Vector Algebra chapter in the past five years of the JEE Main exam.

Year Wise Weightage of Questions: JEE Main Vector Algebra

Sl. No.


Average No. Of Questions Asked

Marks per Question

Total Marks





















To reach your goals, prepare for your JEE Main 2024 exams using Vedantu’s Vector Algebra Notes PDF and The JEE Main Maths Syllabus 2024.

Competitive Exams after 12th Science

Top Concepts to Study in Vector Algebra for JEE Main 2024

Here, you will look at the main topics you should review in Vector Algebra. These crucial topics can truly improve your preparation. Good at them will give you a big advantage in the upcoming test. So, let's discuss the essential topics you need to consider for success in JEE Main 2024.

  • Introduction to Vectors

  • Operations with Vectors

  • Position and Displacement Vectors

  • Vector Components

  • Vector Algebra

  • Scalar and Vector Triple Products

  • Applications of Vectors

  • Equations of Lines and Planes in 3D

  • Geometric Interpretations

  • Applications in Physics and Engineering

  • Vector Equations of Plane and Line

  • Parametric Equations

  • 2D and 3D Geometry Applications

Maths Notes: Chapter-wise links 2024

Download JEE Main Maths Chapter-wise Notes - Free PDF from the table below:

Why Notes of Vector Algebra Important for JEE Main 2024?

As you navigate the intricate path toward conquering JEE Main 2024, the Vector Algebra chapter emerges as a potent cornerstone, infusing your preparation with essential mathematical tools and fostering problem-solving acumen that extends beyond the exam's borders. These notes aren't just a study aid; they're a compass guiding you through the labyrinth of vectors and their real-world applications.

In the tapestry of JEE Main 2024, the Vector Algebra notes thread a narrative of mathematical elegance and pragmatic application. These notes transcend the exam's confines, instilling you with problem-solving prowess, analytical thinking, and an appreciation for how mathematics lays the foundation for scientific understanding.

Here are a few points that justify Why Notes of Vector Algebra Important For JEE Main 2024?

Foundational Concept:

At the heart of calculus, physics, and engineering lies the concept of vectors. These notes lay the groundwork for comprehending vectors' magnitude, direction, and operations.

Geometry and Physics Connection:

Vector Algebra forms an intricate bridge between geometry and physics. It transforms abstract concepts into tangible mathematical tools, making it indispensable for a holistic understanding.

Operational Mastery:

The notes equip you to deftly handle vector operations—addition, subtraction, and scalar multiplication. These operations are crucial for mastering higher mathematics.

Geometric Visualization:

Understanding vector components and their algebraic manipulation enhances your spatial intuition, enabling you to visualize relationships in two and three dimensions.

Applications in Kinematics:

As you delve deeper, you'll realize the profound role vectors play in physics, particularly in describing displacement, velocity, and acceleration—cornerstones of mechanics.

Forces and Equilibrium:

Vector Algebra becomes your ally when dissecting forces, equilibrium, and the intricate dance of physical interactions.

Electromagnetic Insights:

In the realm of electromagnetism, vectors unravel the complexities of electric and magnetic fields, providing insights into charges and currents.

Scalar and Vector Triple Products:

As you progress, you'll grasp the elegance of scalar and vector triple products, delving into deeper mathematical waters.

Coordinate and Parametric Equations:

The chapter's culmination lies in its applicability to coordinate and parametric equations, enriching your understanding of complex curves and surfaces.

As you absorb the contents of these notes, remember that you're not just preparing for an exam—you're cultivating skills that will illuminate your intellectual journey for years to come.

Vector Algebra Formulas to Learn With Notes

JEE Main formulas are important for doing well in the exam. Using them with organized revision notes becomes useful for understanding everything well. While you go over your JEE Main notes, include the related formulas. First, understand why the formula is used by looking at the notes, and then try it on practice problems. This mix helps you understand better, remember more, and get better at solving problems. These are all very important for doing great in JEE Main 2024. You can get the essential JEE Main Maths Formula PDF for free from Vedantu’s website and get higher scores in your JEE Main 2024 Exams.

Important Formulas of Vector Algebra 

1. Vector Representation:

$\mathbf{A} = \langle A_1, A_2, A_3 \rangle$

2. Position Vector:

$\mathbf{r} = \langle x, y, z \rangle = x\mathbf{i} + y\mathbf{j} + z\mathbf{k}$

3. Vector Addition:

$\mathbf{A} + \mathbf{B} = \langle A_1 + B_1, A_2 + B_2, A_3 + B_3 \rangle$

4. Scalar Multiplication:

$k \cdot \mathbf{A} = \langle kA_1, kA_2, kA_3 \rangle$

5. Dot Product:

$\mathbf{A} \cdot \mathbf{B} = A_1B_1 + A_2B_2 + A_3B_3$

6. Cross Product:

$\mathbf{A} \times \mathbf{B} = \langle A_2B_3 - A_3B_2, A_3B_1 - A_1B_3, A_1B_2 - A_2B_1 \rangle$

7. Scalar Triple Product:

$\mathbf{A} \cdot (\mathbf{B} \times \mathbf{C}) = \mathbf{B} \cdot (\mathbf{C} \times \mathbf{A}) = \mathbf{C} \cdot (\mathbf{A} \times \mathbf{B})$

8. Vector Triple Product:

$\mathbf{A} \times (\mathbf{B} \times \mathbf{C}) = (\mathbf{A} \cdot \mathbf{C}) \cdot \mathbf{B} - (\mathbf{A} \cdot \mathbf{B}) \cdot \mathbf{C}$

9. Unit Vector:

$\hat{\mathbf{A}} = \frac{\mathbf{A}}{\|\mathbf{A}\|}$

10. Projection of \(\mathbf{A}\) onto \(\mathbf{B}\):

$\text{proj}_{\mathbf{B}} \mathbf{A} = \frac{\mathbf{A} \cdot \mathbf{B}}{\|\mathbf{B}\|} \cdot \frac{\mathbf{B}}{\|\mathbf{B}\|}$

Explore Further: Supplementary Resources for JEE Main 2024 Vector Algebra

Looking to enhance your JEE Main 2024 Vector Algebra preparation? Explore these Important materials:

  • Practice Papers: Enhance your abilities through focused practice.

  • MockTests: Replicate exam scenarios for increased confidence.

  • Sample Papers: Get acquainted with question formats.

  • Previous Year Question Papers (PYQPs): Understand exam patterns.

Use these tools to improve comprehension and test-taking skills, boosting your JEE Main 2024 performance!

Access the supplementary resources for JEE Main 2024 here:

Prepare with Vedantu’s JEE Main Notes to Raise your Performance

In your journey to conquer JEE Main 2023-24, Vector Algebra Notes are your trusted guide. They simplify complex concepts, highlight key points, and provide practice, making your preparation effective. With Vedantu's JEE Main notes, you will understand better, solve problems confidently, and excel in in the exam. Download the Vector Algebra Revision Notes for FREE to sharpen your skills and triumph in JEE Main 2024.

FAQs on JEE Main - Vector Algebra Notes (Free PDF Download)

1. What are the most important topics included in Vector Algebra Notes for JEE Main 2024?

The most important topics in Vector Algebra Notes for JEE Main 2024 include:

  • Addition, subtraction, and scalar multiplication of vectors.

  • Finding direction cosines and direction ratios.

  • Dot product and cross product of vectors.

  • Vector equations of lines and planes.

  • Applications in physics, mechanics, and engineering.

2. What is the weightage of Vector Algebra Notes for JEE Main 2024?

The weightage of Vector Algebra Notes in JEE Main 2024 is typically around 5-7% of the overall mathematics section, making it an essential but relatively smaller part of the exam.

3. Which is the easiest topic of JEE Main 2024 Vector Algebra Notes?

For many students, finding the magnitude and direction of vectors might be one of the easier topics in Vector Algebra.

4. What is Vector Algebra in the context of JEE Main 2024?

In the context of JEE Main 2024, Vector Algebra refers to the mathematical study of vectors—quantities with both magnitude and direction. It encompasses operations on vectors, their algebraic properties, and applications in physics and engineering.

5. How can I apply the Vector Algebra to solve JEE Main problems?

To apply Vector Algebra to solve JEE Main problems:

  • Represent given quantities as vectors.

  • Perform vector operations (addition, subtraction, scalar multiplication).

  • Use dot product and cross product to solve problems involving angles, areas, and equations.

  • Translate real-world scenarios into vector equations and solve for unknowns.

6. Are there any common mistakes students make in Vector Algebra problems?

Common mistakes students make in Vector Algebra problems include:

  • Incorrectly applying vector operations.

  • Not considering direction when calculating dot or cross products.

  • Miscalculating magnitudes or directions of vectors.

7. What are the expected difficulty level of JEE Main Vector Algebra questions?

Vector Algebra questions in JEE Main can vary in difficulty. Some might involve basic vector operations, while others could require more complex applications of dot and cross products.

8. How To learn using JEE Main 2024 Vector Algebra Notes?

  • Understand vector representations and operations thoroughly.

  • Practice solving a variety of problems to strengthen skills.

  • Focus on applying vector concepts to physics and engineering scenarios.

  • Review real-world applications to solidify your understanding.