CBSE Class 12 Maths Vectors Formula Sheet 2025–26 – Free PDF Download

Vectors are a fundamental concept in CBSE Class 12 Mathematics and are widely used in physics, engineering, and applied mathematics. Understanding vectors and their operations is essential for solving problems in 2D and 3D geometry. To help students revise efficiently, Studentbro.in provides a CBSE Class 12 Maths Vectors Chapter-wise Formula PDF for the academic year 2025–26, available for free download.

This formula sheet is fully aligned with the latest CBSE syllabus and examination pattern, making it an excellent resource for students preparing for board exams.

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Importance of Vectors in CBSE Class 12 Maths

Vectors are used to describe quantities having both magnitude and direction. Questions from vectors often appear in both short-answer and long-answer sections in Class 12 board exams.

Mastering vectors helps students:

• Solve 2D and 3D geometry problems

• Understand scalar and vector operations

• Develop logical reasoning and problem-solving skills

• Prepare for higher studies in mathematics, physics, and engineering

With all vector formulas in one PDF, students can revise quickly and accurately.

What is Included in CBSE Vectors Formula PDF 2025–26

The Vectors Formula PDF by Studentbro.in includes all formulas, definitions, and standard results from the vectors chapters prescribed for Class 12. The content is chapter-wise, easy to understand, and exam-focused.

Chapter-wise Coverage of Vectors Formulas

Chapter 10: Vectors – Basic Definitions and Formulas

The chapter introduces the concept of vectors. The PDF includes:

• Definition of vector

• Zero vector and position vector

• Equal vectors

• Types of vectors: unit vector, co-initial vectors, parallel vectors

• Addition of vectors (triangle and parallelogram law)

• Subtraction of vectors

These are the foundational formulas required for understanding vector algebra.

Scalar Multiplication and Vector Operations – Formula Sheet

The PDF explains all formulas for vector operations:

• Scalar multiplication of a vector

• Addition and subtraction of vectors

• Multiplication by a scalar

• Negative of a vector

• Properties of vector addition and scalar multiplication

These operations form the basis for solving numerical problems.

Dot Product (Scalar Product) – Key Formulas

The scalar product is an important concept in vector algebra. The formula PDF includes:

• Definition: A · B = |A||B|cosθ

• Properties of dot product:

  • Commutative: A · B = B · A

  • Distributive: A · (B + C) = A · B + A · C

  • Scalar multiplication: (kA) · B = k(A · B)

• Angle between two vectors using dot product

These formulas are often used in board exam numerical problems.

Cross Product (Vector Product) – Important Formulas

The vector product is used in 3D vector problems. The PDF includes:

• Definition: A × B = |A||B|sinθ n̂

• Properties of vector product:

  • Anti-commutative: A × B = –(B × A)

  • Distributive: A × (B + C) = A × B + A × C

  • Scalar multiplication: (kA) × B = k(A × B)

• Right-hand rule for direction of cross product

These formulas are essential for solving 3D geometry questions.

Position Vector of a Point – Formula Sheet

The PDF includes all important results related to position vectors:

• If P and Q are points, position vector of P: OP = r

• Position vector of the midpoint of PQ: (OP + OQ)/2

• Position vector of a point dividing a line segment internally in ratio m:n: (n·OP + m·OQ)/(m+n)

These formulas are frequently asked in board exams.

Applications of Vectors in Geometry

The formula sheet provides formulas for:

• Collinearity of points

• Coplanarity of vectors

• Area of a triangle using vectors: ½|AB × AC|

• Vector equation of a line

• Vector equation of a plane

These applications help students solve geometry problems efficiently.

Weightage of Vectors in CBSE Board Exams

Vectors carry important marks in Class 12 board exams. Questions may include:

• Scalar and vector product problems

• Finding angles between vectors

• Midpoint and division point vectors

• 2D and 3D geometry applications

Revision using a formula sheet ensures accuracy and speed during exams.

Benefits of Using Studentbro.in Vectors Formula PDF

• Free PDF download

• Updated for CBSE syllabus 2025–26

• Chapter-wise structured content

• Clear and simple explanations

• Ideal for last-minute revision

• Board exam oriented

Who Should Use This Vectors Formula Sheet

The PDF is ideal for:

• CBSE Class 12 students

• Students preparing for pre-board and board exams

• Teachers and tutors

• Students preparing for competitive exams

How to Download CBSE Vectors Formula PDF from Studentbro.in

Students can download the CBSE Class 12 Maths Vectors Formula PDF from the official website:

Download Link: Vectors Formula

By subscribing to Studentbro.in, students also get access to:

• Chapter-wise notes

• Important questions

• Sample papers

• Revision PDFs

• Previous year question papers

Why Choose Studentbro.in for CBSE Maths Preparation

Studentbro.in is a trusted platform for CBSE students, offering high-quality, updated, and exam-focused study resources. All content is prepared by subject experts according to the latest syllabus.

Key advantages:

• Reliable and exam-oriented content

• Easy-to-download PDFs

• Free and premium resources

• Student-friendly presentation

Tips to Score High in Vectors

• Memorize all vector formulas carefully

• Practice problems using scalar and vector products

• Revise position vector formulas regularly

• Draw neat diagrams for clarity in exams

• Avoid calculation errors

Daily practice with the formula sheet improves accuracy and confidence.

Final Conclusion

Vectors are a highly scoring chapter in CBSE Class 12 Maths if formulas are revised and applied correctly. The CBSE Class 12 Maths Vectors Chapter-wise Formula PDF 2025–26 from Studentbro.in is a complete and reliable revision resource. Download it for free, practice consistently, and strengthen your preparation for board exams.

For more CBSE study material, visit Studentbro.in and start your smart preparation today.