NCERT Class 12 Mathematics Mathematics Part-II: Chapter 4 — VECTOR ALGEBRA
This chapter introduces the fundamental concepts of Vector Algebra, building upon scalar quantities. It defines vectors as quantities possessing both magnitude and direction, contrasting them with scalars which only have magnitude. The chapter explains directed line segments and their representation as vectors, identifying initial and terminal points. It details how to calculate the magnitude of a vector using the distance formula, especially for position vectors in a three-dimensional coordinate system. The text emphasizes the importance of vectors in various scientific and engineering fields, setting the stage for exploring vector operations and properties in subsequent sections. This foundational understanding is crucial for advanced mathematical and physical concepts in Class 12 CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 12 |
| Subject | Mathematics |
| Book | Mathematics Part-II |
| Chapter | Chapter 4 — VECTOR ALGEBRA |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 573 |
Learning outcomes
- Differentiate between scalar and vector quantities.
- Understand the concept of a directed line segment.
- Define and represent vectors using initial and terminal points.
- Calculate the magnitude of a vector, including position vectors.
- Recognize the importance of vectors in mathematics and science.
Vocabulary
| Word | Meaning |
|---|---|
| Scalar | A quantity that has only magnitude. |
| Vector | A quantity that has both magnitude and direction. |
| Directed line | A line with a prescribed direction. |
| Directed line segment | A line segment with a specified direction; a vector. |
| Initial point | The starting point of a vector. |
| Terminal point | The ending point of a vector. |
| Magnitude | The length or size of a vector. |
| Position vector | A vector representing the position of a point with respect to an origin. |
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Practice questions
- Give two examples of scalar quantities. Answer: Examples: Length, mass, time, speed, temperature, work.
- Give two examples of vector quantities. Answer: Examples: Displacement, velocity, acceleration, force, momentum.
- What is the difference between a scalar and a vector? Answer: A scalar has only magnitude, while a vector has both magnitude and direction.
- What are the initial and terminal points of a vector? Answer: The initial point is where the vector starts, and the terminal point is where it ends.
Practice MCQs
Q1. Which of the following is a scalar quantity?
Explanation: Temperature is a scalar quantity as it only has magnitude and no direction.
Q2. A quantity that has both magnitude and direction is called a:
Explanation: By definition, a vector is a quantity possessing both magnitude and direction.
Q3. The distance between the initial and terminal points of a vector is its:
Explanation: The magnitude of a vector is defined as the distance between its initial and terminal points.
Q4. Which of the following represents a vector?
Explanation: A directed line segment, with a specified direction, is a representation of a vector.
Q5. If a point P has coordinates (x, y, z), its position vector from the origin O has magnitude:
Explanation: The magnitude of a position vector OP is calculated using the distance formula in 3D space.
Frequently asked questions
What is the main difference between scalars and vectors?
Scalars have only magnitude (e.g., speed, mass), while vectors have both magnitude and direction (e.g., velocity, force).
What is a directed line segment?
A directed line segment is a part of a line that has a specific direction, starting from an initial point and ending at a terminal point. It represents a vector.
How is the magnitude of a vector defined?
The magnitude of a vector is its length, calculated as the distance between its initial and terminal points.
What is a position vector?
A position vector is a vector that starts from the origin of a coordinate system and ends at a specific point, indicating the point's location.
Can the magnitude of a vector be negative?
No, the magnitude of a vector represents a length, which is always non-negative (zero or positive).
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Topics covered
NCERT Class 12 Mathematics — Mathematics Part-II — Chapter 4 — VECTOR ALGEBRA. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.