This page hosts the the PDF, and hosts the this chapter, the 2026-27 NCERT print of Class 12 Mathematics Chapter 10 Vector Algebra. The textbook chapter carry every example, exercise question and end-of-chapter summary printed in the official textbook. the PDF are free to download.
- What is inside these notes: 4 NCERT sections covering vectors, addition and scalar multiplication, dot product, and cross product, followed by Exercises 10.1 to 10.4 and one Miscellaneous Exercise (67 problems in total).
The chapter is a fixed 5 to 7 mark slot in every CBSE Class 12 Mathematics board paper.
This is the official NCERT Class 12 Mathematics Chapter 10 textbook PDF mapped to the 2026-27 syllabus. Page numbers, exercise numbering, and figure labels match the print edition. Collegedunia hosts the this Class 12 page ad-free for direct download.
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Why Vector Algebra Class 12 PDF Matters for Boards and Entrance
The the resource address this in the same order as the NCERT textbook.
Vector Algebra is one of the few Class 12 chapters where the same concept is tested at three difficulty levels in the same academic year. CBSE asks for a clean 5-mark long answer on projection, area of triangle, or the section formula. JEE Main lifts the same primitives into multi-step problems on the scalar triple product and coplanarity.
The chapter is also a hard prerequisite for Chapter 11 Three Dimensional Geometry, so a weak grasp here compounds across two units worth roughly 14 board marks. Reading the NCERT Chapter 10 PDF cover to cover, including the 30 solved examples, is the most efficient single-source preparation for both exams.
Vector Algebra Video Chapter Walkthrough
Source: Magnet Brains on YouTube
How Collegedunia's Vector Algebra Class 12 PDF Helps You
the chapter notes here is the unaltered NCERT 2026-27 print. What Collegedunia adds around it is the work through layer, exercise breakdown, and the cross-links to solved solutions, revision notes, and the formula sheet for the same chapter. Three concrete benefits:
- Single-tap download in normal and HD quality, no email gate, no advertisement overlay.
- Page-by-page flipbook rendered above, so you can preview a section before downloading the full file.
- Cross-linked study path: every exercise in the table below links to its step-by-step solutions, formula recap, and the matching Exemplar problem set.
What is Inside the NCERT Class 12 Maths Chapter 10 Vector Algebra PDF
The chapter opens with the definition of a vector as a quantity having both magnitude and direction, then introduces the position vector of a point in three-dimensional space.
From there the the PDF works through types of vectors (zero, unit, equal, negative, collinear, coplanar), vector addition by the triangle and parallelogram laws, scalar multiplication, the section formula for the position vector of a point dividing a line segment, and the two products that cover the exercise sets:
the scalar (dot) product and the vector (cross) product. The 30 solved examples are weighted heavily towards angle-between-vectors, projection of one vector on another, finding a unit vector perpendicular to two given vectors, and computing the area of a triangle or parallelogram via the cross product.
NCERT Class 12 Maths Chapter 10 Section-Wise Breakdown
The this chapter address this in the same order as the NCERT textbook.
The four NCERT sections build sequentially. The table below maps each section to the central formula and the page range where its content and exercises sit in the print edition.
| Section | Topic | Pages | Core Formula |
|---|---|---|---|
| 10.1 to 10.3 | Vectors, types of vectors, position vector, direction cosines | 1 to 12 | |a| = √a12 + a22 + a32 ; l2 + m2 + n2 = 1 |
| 10.4 | Addition of vectors, components, scalar multiplication, section formula | 13 to 18 | r = mb + nam + n |
| 10.5 | Scalar (dot) product, projection of a vector | 19 to 26 | a · b = |a||b|cosθ |
| 10.6 | Vector (cross) product, area of triangle and parallelogram | 27 to 36 | a × b = |a||b|sinθ n |
Vector Algebra Class 12 PDF: Exercise-Wise Problem Count
The five exercises move from elementary vector arithmetic to mixed-concept problems that combine dot and cross products with the section formula. Total: 67 problems across these notes, with the Miscellaneous Exercise carrying the highest difficulty.
| Exercise | Focus Area | Problems |
|---|---|---|
| Exercise 10.1 | Direction cosines, classification of vectors | 5 |
| Exercise 10.2 | Vector addition, magnitude, components in 2D and 3D | 19 |
| Exercise 10.3 | Dot product, angle between vectors, projection | 18 |
| Exercise 10.4 | Cross product, area of triangle and parallelogram | 12 |
| Miscellaneous | Mixed dot and cross product, section formula, collinearity, coplanarity | 13 |
Full step-by-step solutions: Vector Algebra NCERT Solutions for Class 12 Maths covers all 67 problems with marking-scheme step weightage.
How Vector Algebra Class 12 PDF Pairs with Chapter 11 Three Dimensional Geometry
Vector Algebra is the algebraic foundation for Three Dimensional Geometry. Direction cosines, the section formula, the dot product (for angle between two lines or a line and a plane), and the cross product (for the normal to a plane defined by two vectors) all reappear in Chapter 11 with identical notation.
Students who read Chapter 10 first, paying attention to the solved examples on projection and on the area of a triangle, find Chapter 11 substantially shorter. Together the two chapters carry around 14 marks in a typical CBSE board paper.
Other Resources for Class 12 Maths Chapter 10 Vector Algebra
- NCERT Notes for Class 12 Maths Chapter 10 Vector Algebra
- NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra
- this Class 12 page Maths Formula Sheet
- the resource Maths Handwritten Notes
- NCERT Exemplar Solutions for Vector Algebra
- NCERT Exemplar Book PDF for Vector Algebra
NCERT Book PDF for Class 12 Maths: All Chapters
Quick links to every Class 12 Mathematics chapter PDF for cross-chapter reading.
| Chapter | NCERT Book PDF |
|---|---|
| Chapter 10 | Vector Algebra NCERT Book PDF |
| Chapter 1 | Relations and Functions NCERT Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Book PDF |
| Chapter 3 | Matrices NCERT Book PDF |
| Chapter 4 | Determinants NCERT Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Book PDF |
| Chapter 6 | Application of Derivatives NCERT Book PDF |
| Chapter 7 | Integrals NCERT Book PDF |
| Chapter 8 | Application of Integrals NCERT Book PDF |
| Chapter 9 | Differential Equations NCERT Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Book PDF |
| Chapter 12 | Linear Programming NCERT Book PDF |
| Chapter 13 | Probability NCERT Book PDF |
the chapter notes: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback - Vector Algebra Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
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