Introduction to CBSE Maths Vectors (Chapter‑Wise)

Mathematics is a core subject in the CBSE Class 12 curriculum. Among the varied chapters in the syllabus, Vector Algebra holds a significant place due to its applications in geometry, physics, and engineering. StudentBro.in presents a comprehensive, chapter‑wise CBSE Maths formula PDF that helps students revise all vector algebra formulas in one organized resource. This PDF is free to download and linked above, enabling effective preparation for the 2025‑26 academic year.

The Vector chapter in CBSE Class 12 introduces learners to the fundamentals of vectors — quantities with both magnitude and direction — and explores how these quantities are manipulated mathematically. Understanding vector formulas helps students solve complex problems in coordinate geometry and 3D geometry. StudentBro.in’s formula PDF ensures that all essential formulas are compiled in a clear, concise format for quick reference.

Direct All Chapter Links to Download MCQ Based Question (PDF)

► Click “Download Here” next to your subject to access the free PDF.

What are Vectors?

A vector is a quantity that has both magnitude and direction. In contrast to scalar quantities (which have only magnitude), vectors are represented by arrows in geometric space, where the length of the arrow denotes magnitude and the arrow’s orientation indicates direction. Examples include displacement, velocity, and force.

Understanding vectors is fundamental to topics in physics and engineering, as well as advanced mathematics. The CBSE Vectors chapter includes definitions, types of vectors, and methods to calculate vector operations. The StudentBro.in Vectors formula PDF includes all these essentials for quick revision.

Subtopics Covered in the Vectors Formula PDF

To facilitate efficient revision, the downloadable formula PDF covers the following major sub‑sections of the Vector Algebra chapter:

1. Basic Definitions and Concepts

This section explains fundamental ideas like vectors, scalars, representation of vectors in coordinate form, and understanding magnitude and direction of vectors.

2. Types of Vectors

Vectors are categorized based on their properties:

• Zero Vector

• Unit Vector

• Equal Vectors

• Collinear Vectors

• Position Vectors

Understanding these helps students identify and work with vector relationships in problems.

3. Addition and Subtraction of Vectors

One of the primary operations in vector algebra is vector addition. When two vectors are added, the resultant vector is determined by placing them head‑to‑tail.

• Graphical Vector Addition

• Component‑wise Addition

• Subtraction of Vectors (similar to addition but with direction reversed)

These formulas help simplify complex vector equations that appear in coordinate problems.

4. Multiplication of a Vector by a Scalar

Scalar multiplication scales a vector by a real number and changes its magnitude without altering its direction (except when multiplied by a negative scalar).

The StudentBro.in PDF lists the rules and formulas for multiplying vectors by scalars, which are frequently used in algebraic simplifications.

5. Direction Cosines and Direction Ratios

In 3D geometry, understanding the direction of a vector requires knowing its orientation with respect to the axes. Direction cosines and direction ratios are essential for this:

• Direction cosines: cos α, cos β, cos γ (angles with x, y, z axes)

• Direction ratios: proportional values that define vector direction

These formulas are crucial in coordinate geometry questions.

6. Dot Product (Scalar Product)

The dot product of two vectors (also called the scalar product) results in a scalar and is defined as:

• A · B = |A||B| cos θ

This operation is useful in finding angles between vectors and determining orthogonality (when dot product is zero).

7. Cross Product (Vector Product)

The cross product of two vectors results in a new vector perpendicular to both original vectors. The magnitude of the cross product is:

• |A × B| = |A||B| sin θ

Cross product formulas are essential for solving spatial geometry problems, including area calculations of parallelograms and triangles formed by vectors.

8. Projection of a Vector on a Line

Vector projection measures how much of one vector lies in the direction of another. The StudentBro.in PDF provides formulas to calculate both scalar and vector projections.

9. Practical Applications and Problem Solving

By using the formulas compiled in the PDF, students can solve vector problems in coordinate geometry, physics applications, and analytical problems faster and with confidence. These formulas also strengthen problem‑solving skills for competitive exams like JEE and CUET.

Why Download the Vectors Formula PDF from StudentBro.in?

StudentBro.in’s chapter‑wise formula PDF allows students to:

• Revision on the go with organized notes

• Save time by having all vector formulas in one place

• Prepare for exams with clarity and confidence

• Boost performance by mastering key vector operations quickly

The formulas are aligned with the 2025‑26 CBSE Maths syllabus, ensuring relevance and accuracy for board exam preparation and daily study routines.

Tips for Using the Vector Formula PDF Effectively

To make the most of your formula PDF:

• Review formulas daily to strengthen recall

• Practice formula‑based problems from past papers

• Combine with NCERT textbook examples for deeper understanding

• Use the formulas to verify answers quickly while solving exercises

Conclusion

The CBSE Maths Vectors Formula PDF (2025‑26) available on StudentBro.in is an essential free tool for Class 12 students. Whether you are revising for board exams or strengthening your basics for competitive test prep, this formula sheet simplifies every core concept of Vector Algebra. Download the PDF now from the link above and ensure you have every important formula at your fingertips.