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

In science and mathematics, basically there are two types of quantities – scalar and
vector quantities. The scalar quantity involves only one value (magnitude) such as
speed, length, mass, area and so on. On the other hand, the vector quantity comprises
more than one value (direction and magnitude) such as velocity, force, acceleration,
weight, displacement, momentum and so on.

In this chapter, you will learn some fundamental concepts about vectors. You will also
learn various operations on vectors and their algebraic and geometric properties.
Vector algebra is used in various fields such as quantum mechanics, wave propagations,
in various oscillators, fluid mechanics, general relativity and much more.

Let’s take a look at topics and sub-topics of Class 12 Maths, Chapter 10, Vector Algebra

10.1 Introduction
10.2 Some Basic Concepts
10.3 Types of Vectors
10.4 Addition of Vectors
10.5 Multiplication of a Vector by a Scalar
10.6 Product of Two Vectors

In Class 12 Maths Chapter 10, you will learn –

Section 10.2 – In this section, you’ll learn basic terms like directed line, line segment,
initial point, terminal point, the magnitude of the vector, position vector, direction
cosines, direction ratios and more.

Section 10.3 – In this section, you’ll study about different types of vectors like zero
vector, unit vector, co-initial vector, collinear vectors, equal vectors, negative of a vector
and free vectors.

Section 10.4 – In this section, you’ll come across the triangle law of vector addition and
different properties of vector addition such as commutative property and associative
property.

Section 10.5 – You will also learn multiplication of a vector by a scalar in this section
along with the negative (or additive inverse) of vector, components of a vector, vector
joining two points and section formula.

Section 10.6 – In this section acquire knowledge about scalar (or dot) product of two
vectors, two important properties of scalar product, and projection of a vector on a line.

For better understanding, examples & solutions are provided along with notes and
several activities. To know more about the Class 12 Maths Chapter 10 Vector
Algebra, you should explore the exercises below. You can also download the Vector
Algebra Class 12 NCERT Solutions PDF, solved by expert Maths trainers.

Also, solve miscellaneous exercises of Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise on Chapter 10.

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