RD Sharma Class 12 Exercise 22.1 Algebra of Vectors Solutions Maths

RD Sharma Class 12 Exercise 22.1 Algebra of Vectors Solutions Maths - Download PDF Free Online

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.

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RD Sharma Class 12 Solutions Chapter22 Algebra of vectors - Other Exercise

Algebra of Vectors Excercise: 22.1

Algebra of vector exercise 22.1 question 1 (i)

Answer:

The required vector is $\vec{OP}$
Hint:
By the concept of magnitude and direction of vectors.
Given:
Displacement = 40km
Solution:
The vector $\vec{OP}$ represents the required displacement vector.

Algebra of vector exercise 22.1 question 1 (ii)

Answer:

The required vector is $\vec{OQ}$ .
Hint:
By the concept of magnitude and direction of vectors.
Given:
Displacement = 50km
Solution:
The vector $\vec{OQ}$ 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 are $\vec{a} ,\vec{d} ; \vec{x},\vec{z},\vec{b} ;\vec{c},\vec{y}$
Hint:
When two or more vectors parallel to same line irrespective of their magnitude and direction $\vec{a} ,\vec{d} ; \vec{x},\vec{z},\vec{b} ;\vec{c},\vec{y}$ .
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 $\vec{a} ,\vec{d} ; \vec{x},\vec{z},\vec{b} ;\vec{c},\vec{y}$

Algebra of Vector exercise 22.1 question 4 (ii)

Answer:

Equal vectors are $\vec{b},\vec{x};\vec{c},\vec{y};\vec{a},\vec{d}$
Hint:
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 $\vec{b},\vec{x};\vec{c},\vec{y};\vec{a},\vec{d}$

Algebra of Vector exercise 22.1 question 4 (iii)

Answer:

Initial vectors are $\vec{a},\vec{y},\vec{z}$
Hint:
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 $\vec{a},\vec{y},\vec{z}$

Algebra of Vector exercise 22.1 question 4 (iv)

Answer:

$\vec{b},\vec{z};\vec{x},\vec{z}$ are collinear but not equal
Hint:
Collinear vectors are parallel to the same line
Given:
ABCDEF is a regular hexagon

Solution:
The vector which are collinear but not equal are $\vec{b},\vec{z};\vec{x},\vec{z}$

Algebra of vectors exercise 22.1, question 5 (i)

Answer:

True
Hint:
When two or more vectors parallel to the same line irrespective of their magnitude and direction are called collinear vector
Given:
Two vectors $\vec{a}$ & $\vec{a}$
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:

True
Hint:
When two or more vectors parallel to the same line irrespective of their magnitude and direction are called collinear vector
Given:
Two vectors $\vec{a}$ & $\vec{b}$
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:

True
Hint:
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:

False
Hint:
When two or more vectors parallel to the same line irrespective of their magnitude and direction are called collinear vector
Given:
Two vectors $\vec{a}$ & $\vec{b}$
Solution:
False, two vectors having same magnitude need not be collinear

Algebra of vectors exercise 22.1, question 5 (v)

Answer:

False
Hint:
When two or more vectors parallel to the same line irrespective of their magnitude and direction are called collinear vector
Given:
Two vectors $\vec{a}$ & $\vec{b}$
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.

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Frequently Asked Question (FAQs)

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