The NCERT solutions for the questions given in Chapter 10, Vector Algebra, of the Class 12 NCERT textbooks are given here. In this chapter students learn about the difference between a scalar and a vector quantity, their properties, operations of vectors etc,. The topic has an important role in helping the students score high marks not only in the board exams but also the competitive exams.

It is important to be prepared for the various problems asked during the 12th board examination. Solving through different exercises and problem sets give students the confidence to write the exams better. These class 12 NCERT solutions for Vector Algebra are very easy to understand. Students can also avail these NCERT solutions and download it for free to practice them offline as well.

### Download P DF of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra

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## NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra

The major concepts of Maths covered in Chapter 10- Vector Algebra of NCERT Solutions for Class 12 includes:

10.1 Introduction

10.2 Basic Concepts

- Position Vector
- Direction Cosines

10.3 Types of Vectors

- Zero Vector
- Unit Vector
- Coinitial Vectors
- Collinear Vectors
- Equal Vectors
- Negative of a Vector

10.4 Addition of Vectors

- Properties of vector addition

10.5 Multiplication of a Vector by a Scalar

10.5.1 Components of a vector

10.5.2 Vector joining two points

10.5.3 Section formula

10.6 Product of Two Vectors

10.6.1 Scalar (or dot) product of two vectors

10.6.2 Projection of a vector on a line

10.6.3 Vector (or cross) product of two vectors

Exercise 10.1 Solutions 5 Questions

Exercise 10.2 Solutions 19 Questions

Exercise 10.3 Solutions 18 Questions

Exercise 10.4 Solutions 12 Questions

Miscellaneous Exercise On Chapter 10 Solutions 19 Questions

## NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra

The chapter Vector Algebra belongs to the unit Vectors and Three â€“ Dimensional Geometry, that adds up to 14 marks of the total marks. There are 4 exercises along with a miscellaneous exercise in this chapter to help students understand the concepts related to Vectors and Vector Algebra clearly. Some of the topics discussed in the tenth Chapter of NCERT Solutions for Class 12 Maths are as follows:

- The scalar components of a vector are its direction ratios, and represent its projections along the respective axes.
- The magnitude (r), direction ratios (a, b, c) and direction cosines (l, m, n) of any vector are related as l=(a/r), m=(b/r) n=(c/r)
- The vector sum of the three sides of a triangle taken in order is 0.
- The vector sum of two coinitial vectors is given by the diagonal of the parallelogram whose adjacent sides are the given vectors.
- The multiplication of a given vector by a scalar Î», changes the magnitude of the vector by the multiple |Î»|, and keeps the direction same (or makes it opposite) according as the value of Î» is positive (or negative).

The other concepts and topics explained in the chapter can be understood by going through the Chapter 10 of the NCERT textbook for class 12.

### Key Features of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra

Studying the Vector Algebra of Class 12 enables the students to understand the following:

Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.