##### Tallentex 2025 - ALLEN's Talent Encouragement Exam

ApplyRegister for Tallentex '25 - One of The Biggest Talent Encouragement Exam

Edited By Satyajeet Kumar | Updated on Jan 24, 2022 06:18 PM IST

The condition of the class 12 students is ineffable as they are stuck with homework completion and board exam preparations. It is essential for them to follow a top-rated and the most trusted solution book for reference. The arrival of doubts while solving mathematical sums cannot be avoided. For chapters like the Algebra of Vectors, the RD Sharma Class 12th Exercise 22.1 is very useful.

**JEE Main 2025: Sample Papers | Mock Tests | PYQs | Study Plan 100 Days**

**JEE Main 2025: Maths Formulas | Study Materials**

**JEE Main 2025: Syllabus | Preparation Guide | High Scoring Topics **

Algebra of vector exercise 22.1 question 1 (i)

Answer:

The required vector is

Hint:

By the concept of magnitude and direction of vectors.

Given:

Displacement = 40km

Solution:

The vector represents the required displacement vector.

Algebra of vector exercise 22.1 question 1 (ii)

The required vector is .

Hint:

By the concept of magnitude and direction of vectors.

Given:

Displacement = 50km

Solution:

The vector represents the required displacement vector.

Algebra of vector exercise 22.1 question 2 (i)

Answer:

Mass 15kg is a scalar quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

Mass = 15kg.

Solution:

We know that 15 kg is a mass and mass is a scalar quantity as it is one dimensional measurement of a quantity.

Algebra of vector exercise 22.1 question 2 (ii)

Answer:

20kg- weight is a vector quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

Weight = 20kg – weight

Solution:

We know that 20kg – weight is force. And force is a vector quantity.

Algebra of Vectors exercise 22.1 question 2 (iv)

Answer:

10 meter south- east is a vector quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

Direction displacement = 10 meter south- east.

Solution:

Here in 10 meter South – east, 10 meter denotes the displacement And South- east is the direction which is a vector quantity.

Algebra of Vectors exercise 22.1 question 2 (v)

Answer:

50 m/sec² is an acceleration i.e., scalar quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given: 50 m/sec²

Solution-

50 m/sec² is scalar quantity as it represents an acceleration.

Algebra of Vectors exercise 22.1 question 3 (i)

Answer:

Time period is scalar quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

We have time period mentioned here.

Explanation:

Time period is a scalar quantity which do not have magnitude and direction.

Algebra of Vectors exercise 22.1 question 3 (ii)

Answer:

Distance is scalar quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

We have Distance mentioned here.

Solution:

Distance is a scalar quantity as because it doesn’t have any direction.

Algebra of Vectors exercise 22.1 question 3 (iii)

Answer:

Displacement is scalar quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

We have time displacement mentioned here.

Solution:

Displacement is a scalar quantity which do not have magnitude and direction.

Algebra of Vectors exercise 22.1 question 3 (iv)

Answer:

Force is vector quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

We have force mentioned here.

Solution:

Force is a scalar quantity it has both magnitude and direction.

Algebra of Vectors exercise 22.1 question 3 (v)

Answer:

Work is a scalar quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

We have work mentioned here.

Solution:

Work is a scalar quantity as it doesn’t have any direction.

Algebra of Vectors exercise 22.1 question 3 (vi)

Answer:

Velocity is a vector quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

We have velocity mentioned here.

Solution:

Velocity is a vector quantity it has both magnitude and direction.

Algebra of Vectors exercise 22.1 question 3 (vii)

Answer:

Acceleration is a vector quantity.Hint:

The quantities which have only magnitude and which are not related to any fixed direction in space are called scalar quantities or simply scalars.

The quantities which have both magnitude and direction are called vector quantities or simply vectors.

Given:

We have acceleration mentioned here.

Solution:

Acceleration is a vector quantity it has both magnitude and direction.

Algebra of Vector exercise 22.1 question 4 (i)

Answer:

Collinear vectors areHint:

When two or more vectors parallel to same line irrespective of their magnitude and direction .

Given:

ABCD is a regular hexagon.

Solution:

Vectors having the same or parallel supports are called collinear vectors.

In the given figure,

Collinear vectors are

Algebra of Vector exercise 22.1 question 4 (ii)

Answer:

Equal vectors areHint:

Two or more vectors are equal when they have the same length and they point in the same direction

Given:

ABCDEF is a regular hexagon

Solution:

Vectors having the same magnitude and direction are called equal vector.

In the given figure the equal vectors are

Algebra of Vector exercise 22.1 question 4 (iii)

Answer:

Initial vectors areHint:

When or more vectors have the same starting point are called the co-initial vectors

Given:

ABCDEF is a regular hexagon

Solution:

Vectors having the same initial points are called co-initial vectors.

In the given figure the co-initial vectors are

Algebra of Vector exercise 22.1 question 4 (iv)

Answer:

are collinear but not equalHint:

Collinear vectors are parallel to the same line

Given:

ABCDEF is a regular hexagon

Solution:

The vector which are collinear but not equal are

Algebra of vectors exercise 22.1, question 5 (i)

Answer:

TrueHint:

When two or more vectors parallel to the same line irrespective of their magnitude and direction are called collinear vector

Given:

Two vectors &

Solution:

True, as vectors having the same and parallel support so that these vectors are collinear.

Algebra of vectors exercise 22.1, question 5 (ii)

Answer:

TrueHint:

When two or more vectors parallel to the same line irrespective of their magnitude and direction are called collinear vector

Given:

Two vectors &

Solution:

True, as vectors having the same and parallel support so that these vectors are collinear.

Algebra of vectors exercise 22.1, question 5 (iii)

Answer:

TrueHint:

Zero vector is a force of zero newton in all direction

Given:

Zero vector is unique

Solution:

True, as two zero vector are equal.

Algebra of vectors exercise 22.1 question 5 (iv)

Answer:

FalseHint:

When two or more vectors parallel to the same line irrespective of their magnitude and direction are called collinear vector

Given:

Two vectors &

Solution:

False, two vectors having same magnitude need not be collinear

Algebra of vectors exercise 22.1, question 5 (v)

Answer:

FalseHint:

When two or more vectors parallel to the same line irrespective of their magnitude and direction are called collinear vector

Given:

Two vectors &

Solution:

False, as two collinear vectors are equal only if they have same magnitude and same direction, instead of their initial points.

Chapter 22, Algebra of Vectors in class 12 mathematics, consists of nine exercises, ex 22.1 to ex 22.9. The first exercise, ex 22.1, contains 24 questions that must be solved by the students. The concepts included in this exercise are basic ideas on Vectors, Scalar and Vector quantities, and Collinear vector. All the sums are under the Level 1 category, which denotes that they are not much complex to solve. RD Sharma solutions Therefore, the students can try the sums on their own and recheck their answers with the ones given in the RD Sharma Class 12 Chapter 22 Exercise 22.1 reference guide.

Apart from the 24 questions given in the class 12 mathematics textbook, the RD Sharma Class 12th Exercise 22.1 solution book offers many practice questions too. When the students work out these sums, they will develop a deeper understanding and clarity of the concept of the vector. Moreover, they can clarify their doubts while doing homework, assignment, and preparing for public and JEE mains exam. Regular updates are made in the Class 12 RD Sharma Chapter 22 Exercise 22.1 Solution according to the NCERT syllabus.

The previous batch, class 12 students have faced many questions from the RD Sharma books in their public exams. And it is a known fact that most of the teachers pick questions from the RD Sharma Class 12 Solutions Algebra of Vectors Ex 22.1 to conduct tests and exams. Therefore, the students who use this set of books from day one of their exam preparation tend to achieve more marks effortlessly.

Students can grab the opportunity of obtaining the RD Sharma Class 12th Exercise 22.1 book for free from the Career 360 website. They need not carry a big solution guide to their schools and tuitions. The PDF material of this solution book available in smartphones reduces the burden in their bag.

As the solutions are provided by teachers who possess expertise in the respective field, all the answers are accurate. Therefore, the RD Sharma Class 12 Solutions Chapter 22 book solves many problems and struggles of the class 12 students. Now, it is your time to download this set of resource materials for your reference and doubt clarifications.

**RD Sharma Chapter wise Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Where can the class 12 students refer to when they have doubts regarding the Algebra of Vectors concept?

The RD Sharma Class 12th Exercise 22.1 solution guide is the best resource to refer to when the students face doubts in the Algebra of Vectors concept.

2. Where is the complete set of RD Sharma books available?

You can find the complete set of the RD Sharma solution books on the Career 360 website.

3. How much does it cost to own the RD Sharna books in PDF format?

The PDF format of the RD Sharma books is available for free on the Career 360 website. Hence you need not pay to obtain this set of solution books.

4. Is the Algebra of Vectors hard to learn for the class 12 students?

Every concept seems to be hard when the students have no clarity in it. The RD Sharma Class 12th Exercise 22.1 reference book helps the students to learn the concept in-depth.

5. Are the RD Sharma books currently available on the Career 360 website updated?

Every RD Sharma book on the Career 360 website is updated according to the recent NCERT syllabus.

Get answers from students and experts

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 10% OFF : Use promo code: 'C360SPL10'. Limited Period Offer!

As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE

News and Notifications

Back to top