RD Sharma Class 12 Maths Solutions Chapter 23 - Algebra of Vectors

Q: 1. What are the types of vectors?

There are many types of vectors such as –Zero vector - A vector whose initial and terminal points coincide, is called a zero vector (or null vector).Unit vector - A vector whose magnitude is unity (i.e., 1 unit) is called a unit vector.Coinitial vector - Two or more vectors having the same initial point are called coinitial vectors.Collinear vectors - Two or more vectors are said to be collinear if they are parallel to the same line, irrespective of their magnitudes and directions.Equal vectors - Two vectors are said to be equal if they have the same magnitude and direction regardless of the positions of their initial points.Negative of a vector - A vector whose magnitude is the same as that of a given vector but direction is opposite to that of it, is called negative of the given vector.These are the important factors that are discussed in depth in the RD Sharma book of Class 12 Mathematics.

RD Sharma Solutions

RD Sharma Class 12 Maths Solutions Chapter 23 - Algebra of Vectors

Last updated date: 26th Apr 2024

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RD Sharma Solutions for Class 12 Maths Chapter 23 - Algebra of Vectors - Free PDF Download

Vector algebra is the method of performing algebraic operations on vectors, most specifically Euclidean vectors. In Mathematics, operations on vectors in two-dimensional and three-dimensional space are widely covered. These topics are discussed in RD Sharma in a simple manner that every beginner would be able to understand. However, RD Sharma is a choice you should be working on to prepare for your upcoming board exams and competitive exams on the subject of vector algebra. Algebra of vectors RS Sharma solutions provides a higher level of difficulty on their questions, allowing you to look deeper into the topic.

Vedantu provides a free PDF on Algebra of Vectors Class 12 RD Sharma Solutions according to the CBSE curriculum. This PDF also has a lot of exercises and practice problems to make students more confident about the concept.

Brief Idea About the Chapter

Class 12 Chapter algebra of vectors is the 23rd Chapter of the RD Sharma book while it is the 10th Chapter of the NCERT book. This Chapter mainly deals with vectors and scalars. This Chapter explains how there are various quantities that have magnitude and direction. Victor can be defined as a quantity that has both magnitude and direction but no position. Examples of such quantities are velocity and acceleration. A quantity that involves only one value or magnitude which is a real number, such quantities are called scalars. For example time, distance, speed et cetera.

This Chapter explains in-depth the arithmetic operations that can be performed on vectors and their algebraic and geometric properties.

An interesting fact about vectors- In 1880 Josiah Willard Gibbs and Oliver Heaviside, created vector analysis to explain the new laws of electromagnetism. Gifts printed or treaties entitled elements of vector analysis This analysis is considered extremely important in the study of the algebra of vectors.

Topics Covered In This Chapter

Directed line segment,
position of vector,
direction cosines,
types of vectors,
addition of vectors,
properties of vector addition,
multiplication of a vector by a scalar,
components of a vector,
vector joining two points,
section formula,
product of two vectors,
scalar product of two vectors,
projection of a vector on the line,
vector or cross product of two vectors.

RD Sharma develops a comprehensive understanding of all of these concepts. The book contains an innumerable number of practice questions and HOTS Which are tailored to assess students’ analytical and creative skills. These are higher aptitude questions that can only be solved if the student has in-depth knowledge of all of the concepts mentioned above. Sharma is based on the CBSE curriculum. In order to get a good percentage in the board exams, RD Sharma is the best option to practice Mathematics or any other subject. The excess number of questions given in the book is for students so that they can solve any problem in a fraction of seconds and so that they have all the formulas at the tips of their fingers. The book is great for board exams as After a student has solved all the questions he or she is prepared to solve any problem in a time-efficient manner. To make the learning process easier Vedant has provided all the solutions of RD Sharma’s book of the Chapter algebra of vectors. The study material is easily accessible on the Internet and all the links are available for free download.

FAQs on RD Sharma Class 12 Maths Solutions Chapter 23 - Algebra of Vectors

1. What are the types of vectors?

There are many types of vectors such as –

Zero vector - A vector whose initial and terminal points coincide, is called a zero vector (or null vector).
Unit vector - A vector whose magnitude is unity (i.e., 1 unit) is called a unit vector.
Coinitial vector - Two or more vectors having the same initial point are called coinitial vectors.
Collinear vectors - Two or more vectors are said to be collinear if they are parallel to the same line, irrespective of their magnitudes and directions.
Equal vectors - Two vectors are said to be equal if they have the same magnitude and direction regardless of the positions of their initial points.
Negative of a vector - A vector whose magnitude is the same as that of a given vector but direction is opposite to that of it, is called negative of the given vector.

These are the important factors that are discussed in depth in the RD Sharma book of Class 12 Mathematics.

2. Why is the algebra of vectors an important Chapter?

Vector algebra or algebra of vectors is an extremely important Chapter as it contributes to our day-to-day lives. Knowledge of this helps to determine certain distance speed, area volume velocity, and acceleration. This chapter mainly deals with vectors and scalars. It is prescribed by the CBSE curriculum and RD Sharma is based on the syllabus provided by the CBSE and it provides innumerable practice questions that help in understanding the concept in depth.

3. What are the important topics covered in the algebra of vectors/vector algebra?

Important topics covered are as follows – Directed line segment, the position of vector, direction cosines, types of vectors, the addition of vectors, properties of vector addition, multiplication of a vector by a scalar, components of a vector, vector joining two points, section formula, a product of two vectors, scalar product of two vectors, projection of a vector on the line, vector or cross product of two vectors.

4. What are the examples of vectors and scalars?

Force, velocity, acceleration, displacement, and momentum are some of the examples of vectors, while, length, mass, time, distance, speed, area, volume, temperature, work, money, voltage, density, resistance, etc.

5. Are the questions given in RD Sharma difficult to solve?

The practice questions given in RD Sharma are tailored in a way that increases critical thinking and analytical abilities. These questions will help students to perform well in the exams. All the questions are available on Vedantu’s website along with their solutions.