NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra is designed and prepared by the best teachers of ANAND CLASSES. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

Chapter 10 – Vector Algebra covers multiple exercises. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. This will prove to be most helpful to you in your home assignments as well as practice sessions.

Download the pdf of NCERT Solutions for Class 12 Maths Chapter 10 – Vector Algebra

Major Concepts of 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 include

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

NCERT Solutions for Class 12 Maths Chapter 10 Exercise-wise

• 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

Important Topic of NCERT Solutions for Class 12 Maths Chapter 10 – Vector Algebra

The chapter Vector Algebra belongs to the unit Vectors and Three-Dimensional Geometry, which 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:

1. The scalar components of a vector are its direction ratios and represent its projections along the respective axes.
2. 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)
3. The vector sum of the three sides of a triangle taken in order is 0.
4. The vector sum of two coinitial vectors is given by the diagonal of the parallelogram whose adjacent sides are the given vectors.
5. The multiplication of a given vector by a scalar λ changes the magnitude of the vector by the multiple |λ| and keeps the direction the same (or makes it opposite) accordingly, as the value of λ is positive (or negative).

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

Features of NCERT Solutions for Class 12 Maths Chapter 10 – Vector Algebra

By studying the Vector Algebra of Class 12 using the NCERT Solutions enables the students to understand the following topics :

• 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, the 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, the scalar triple product of vectors.

Frequently Asked Questions (FAQs) on NCERT Solutions for Class 12 Maths Chapter 10

Q1

How many questions are present in each exercise of NCERT Solutions for Class 12 Maths Chapter 10?

The number of questions in each exercise of NCERT Solutions for Class 12 Maths Chapter 10 is listed below:

• Exercise 10.1 – 5 Questions
• Exercise 10.2 – 19 Questions
• Exercise 10.3 – 18 Questions
• Exercise 10.4 – 12 Questions
• Miscellaneous Exercise – 19 Questions

Q2

What are the major concepts discussed in NCERT Solutions for Class 12 Maths Chapter 10?

The major concepts discussed in NCERT Solutions for Class 12 Maths Chapter 10 are as follows:

• 10.1 – Introduction
• 10.2 – Basic Concepts
• 10.3 – Types of Vectors
• 10.4 – Addition of Vectors
• 10.5 – Multiplication of a vector by a scalar

Q3

Where can I get exercise-wise answers to NCERT Solutions for Class 12 Maths Chapter 10?

The solutions for both chapter-wise and exercise-wise problems are available in PDF format in ANAND CLASSES’S. It can be referred to by the students while solving problems to get their doubts cleared instantly.

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