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NCERT Solutions for Exercise 10.1 Class 12 Maths Chapter 10 - Vector Algebra

NCERT Solutions for Exercise 10.1 Class 12 Maths Chapter 10 - Vector Algebra

Edited By Ramraj Saini | Updated on Dec 04, 2023 08:47 AM IST | #CBSE Class 12th

NCERT Solutions For Class 12 Maths Chapter 10 Exercise 10.1

NCERT Solutions for Exercise 10.1 Class 12 Maths Chapter 10 Vector Algebra are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for exercise 10.1 Class 12 Maths chapter 10 introduces the concepts of Vector Algebra. Some of the concepts dealt with in the chapter Vector Algebra are already covered in NCERT Class 11 Physics Syllabus. Exercise 10.1 Class 12 Maths covers the basic concepts of representing a vector graphically and about collinear, coinitial, and equal vectors. Practising the NCERT solutions for Class 12 Maths chapter 10 exercise 10.1 is important from the CBSE Class 12 Board Exam point of view. For the board exam, you can expect questions from Class 12 Maths chapter 10 exercise 10.1.

This Story also Contains
  1. NCERT Solutions For Class 12 Maths Chapter 10 Exercise 10.1
  2. Access NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1
  3. Vector Algebra Class 12 Chapter 10 Exercise 10.1
  4. More About NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1
  5. Key Features Of NCERT Solutions for Exercise 10.1 Class 12 Maths Chapter 10
  6. Also see-
  7. NCERT Solutions Subject Wise
  8. Subject Wise NCERT Exemplar Solutions

The concepts covered in Class 12 Maths chapter 10 exercise 10.1 solutions are also helpful for the preparation of competitive exams like JEE Main. Class 12th Maths chapter 10 exercise 10.1 is useful for the NEET Physics Syllabus, as the problems in Physics use the concepts of Vector Algebra. 12th class Maths exercise 10.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

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Access NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1

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Vector Algebra Class 12 Chapter 10 Exercise 10.1

Question:1 Represent graphically a displacement of 40 km, 30 \degree east of north.

Answer:

Represent graphically a displacement of 40 km, 30 \degree east of north.

N,S,E,W are all 4 direction north,south,east,west respectively.

\underset{OP}{\rightarrow} is displacement vector which \left | \underset{OP}{\rightarrow} \right |

= 40 km.

\underset{OP}{\rightarrow} makes an angle of 30 degrees east of north as shown in the figure.

1626668157287

Question:2 (1) Classify the following measures as scalars and vectors.

10Kg

Answer:

10kg is a scalar quantity as it has only magnitude.

Question:2 (2) Classify the following measures as scalars and vectors. 2 meters north west

Answer:

This is a vector quantity as it has both magnitude and direction.

Question:2 (3) Classify the following measures as scalars and vectors. 40 \degree

Answer:

This is a scalar quantity as it has only magnitude.

Question:2 (4) Classify the following measures as scalars and vectors. 40 watt

Answer:

This is a scalar quantity as it has only magnitude.

Question:2 (5) Classify the following measures as scalars and vectors. 10 ^{-19} \: \: coulomb

Answer:

This is a scalar quantity as it has only magnitude.

Question:2 (6) Classify the following measures as scalars and vectors. 20 m/s^2

Answer:

This is a Vector quantity as it has magnitude as well as direction.by looking at the unit, we conclude that measure is acceleration which is a vector.

Question:3 Classify the following as scalar and vector quantities.
(1) time period

Answer:

This is a scalar quantity as it has only magnitude.

Question:3 Classify the following as scalar and vector quantities.

(2) distance

Answer:

Distance is a scalar quantity as it has only magnitude.

Question:3 Classify the following as scalar and vector quantities.

(3) force

Answer:

Force is a vector quantity as it has both magnitudes as well as direction.

Question:3 Classify the following as scalar and vector quantities.
(4) velocity

Answer:

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

Question:3 Classify the following as scalar and vector quantities.

(5) work done

Answer:

work done is a scalar quantity, as it is the product of two vectors.

Question:4 In Fig 10.6 (a square), identify the following vectors.
(1) Coinitial

1626668486601

Answer:

Since vector \vec{a} and vector \vec{d} are starting from the same point, they are coinitial.

Question:4 In Fig 10.6 (a square), identify the following vectors.
(2) Equal

Answer:

Since Vector \vec{b} and Vector \vec{d} both have the same magnitude and same direction, they are equal.

Question:4 In Fig 10.6 (a square), identify the following vectors.

(3) Collinear but not equal

Answer:

Since vector \vec{a} and vector \vec{c} have the same magnitude but different direction, they are colinear and not equal.

Question:5 Answer the following as true or false.
(1) \vec a and -\vec a are collinear.

Answer:

True, \vec a and -\vec a are collinear. they both are parallel to one line hence they are colinear.

Question:5 Answer the following as true or false.
(2) Two collinear vectors are always equal in magnitude.

Answer:

False, because colinear means they are parallel to the same line but their magnitude can be anything and hence this is a false statement.

Question:5 Answer the following as true or false.

(3) Two vectors having same magnitude are collinear.

Answer:

False, because any two non-colinear vectors can have the same magnitude.

Question:5 Answer the following as true or false.

(4) Two collinear vectors having the same magnitude are equal.

Answer:

False, because two colinear vectors with the same magnitude can have opposite direction

More About NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1

The NCERT book Class 12 Maths chapter vector algebra has a total of 5 exercises including miscellaneous. Exercise 10.1 Class 12 Maths covers solutions to 5 main questions and their sub-questions. The second question of Class 12 Maths chapter 10 exercise 10.1 is related to classifications as scalars and vectors and the 3rd, 4th, and 5th questions of NCERT Solutions for Class 12 Maths chapter 10 exercise 10.1 are related to collinear, equal, and coinitial vectors.

Read Also| Vector Algebra Class 10 Chapter 10 Notes

Benefits of NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1

  • The Class 12th Maths chapter 10 exercise is solved in detail by subject matter experts and these are presented in an easy manner.
  • Students can practice exercise 10.1 Class 12 Maths to prepare for exams.
  • The NCERT Solutions for Class 12 Maths chapter 10 exercise 10.1 gives more clarifications of the concepts covered.
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Key Features Of NCERT Solutions for Exercise 10.1 Class 12 Maths Chapter 10

  • Comprehensive Coverage: The solutions encompass all the topics covered in ex 10.1 class 12, ensuring a thorough understanding of the concepts.
  • Step-by-Step Solutions: In this class 12 maths ex 10.1, each problem is solved systematically, providing a stepwise approach to aid in better comprehension for students.
  • Accuracy and Clarity: Solutions for class 12 ex 10.1 are presented accurately and concisely, using simple language to help students grasp the concepts easily.
  • Conceptual Clarity: In this 12th class maths exercise 10.1 answers, emphasis is placed on conceptual clarity, providing explanations that assist students in understanding the underlying principles behind each problem.
  • Inclusive Approach: Solutions for ex 10.1 class 12 cater to different learning styles and abilities, ensuring that students of various levels can grasp the concepts effectively.
  • Relevance to Curriculum: The solutions for class 12 maths ex 10.1 align closely with the NCERT curriculum, ensuring that students are prepared in line with the prescribed syllabus.
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NCERT Solutions Subject Wise

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Frequently Asked Question (FAQs)

1. What does the initial question of exercise 10.1 Class 12 Maths signify?

The question asks to represent a vector from a reference. Here the reference direction is north and the vector is lying 30 degrees clockwise to the north(towards east). The magnitude of the vector is represented by choosing a scale. For example 1unit=10Km, then 40Km=4 units.

2. In the second question of Class 12 Maths exercise 10.1, how we understood that the given quantity is a vector?

The unit of the quantity is given. The given unit meter per second square represents acceleration. And acceleration is a vector quantity. The concepts of acceleration are covered in the high school Class and also in Class11.

3. How to identify that the given vectors are equal?

If the given vectors have the same magnitude and point towards the same directions then these vectors are equal

4. Can two collinear vectors have different directions?

Yes, two collinear vectors can be in the same direction or in opposite directions.

5. Is it a necessary condition for collinear vectors to have the same magnitude?

No, collinear vectors can have different magnitudes.

6. In the 3rd question of NCERT Solutions for Class 12 Maths chapter 10 exercise 10.1 we come across the term force. What is the unit for force?

The unit of force is Newton and is represented by N.

7. Is power a vector quantity?

No, power is a scalar quantity. Power has magnitude but no direction

8. What questions are expected for exams from Class 12 Maths chapter 10 exercise 10.1?

There may be questions to identify collinear and equal vectors and also to classify the given quantity as scalars and vectors. 

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Have a question related to CBSE Class 12th ?
i upload 12th board result screenshot in ncweb form from the cbse site so it is valid

hello mahima,

If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.

hope this helps.

Read Complete Answer
Ashvadha 12 July,2024
Kya mujhe class 12 ka important question milega jo exam mai per year puche jate hai

Hello Akash,

If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.

You can get the Previous Year Questions (PYQs) on the official website of the respective board.

I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

Thank you and wishing you all the best for your bright future.

Read Complete Answer
kumardurgesh1802 10 July,2024
I have completed my 12th with arts cbse. I want to repeat my 12th with pcmb. How to become a private candidate and what are deadline to be able to appear in 2025 exam?

Hello student,

If you are planning to appear again for class 12th board exam with PCMB as a private candidate here is the right information you need:

  • No school admission needed! Register directly with CBSE. (But if you want to attend the school then you can take admission in any private school of your choice but it will be waste of money)
  • You have to appear for the 2025 12th board exams.
  • Registration for class 12th board exam starts around September 2024 (check CBSE website for exact dates).
  • Aim to register before late October to avoid extra fees.
  • Schools might not offer classes for private students, so focus on self-study or coaching.

Remember , these are tentative dates based on last year. Keep an eye on the CBSE website ( https://www.cbse.gov.in/ ) for the accurate and official announcement.

I hope this answer helps you. If you have more queries then feel free to share your questions with us, we will be happy to help you.

Good luck with your studies!

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kumardurgesh1802 10 July,2024
I passed my 12th cbse boards in 2023 , and first time appear for jee mains and advance in 2024 so , am i eligible for 2025 jee mains and advance ?

Hello Aspirant , Hope your doing great . As per your query , your eligible for JEE mains in the year of 2025 , Every candidate can appear for the JEE Main exam 6 times over three consecutive years . The JEE Main exam is held two times every year, in January and April.

Read Complete Answer
satyamercedes0626 23 July,2024
I've passed my class 12th board exam from cbse in PCB in 2024. Now I'll give mathematics exam from cbse as a additional subject in 2025. However, they'll provide separate marksheet for maths. Will i be eligible for jee?? And how I'll fill the form??

Hi there,

Hope you are doing fine

Yes you are certainly eligible for giving the jee exam in the year 2025. You must pass the maths exam with at least 75% criteria as required by jee and provide the marksheet and the passing certificate while registering for the exam.


Pursuing maths as an additional subject while taking biology as your main subject does not offer any hindrance in you appearing for the jee examination. It is indeed an privilege to pursue both maths and biology as the subjects and prepare for the same.

There will be no issue in filling the form while registering for the exam as it will only require your basic details and marksheet which you can provide by attaching the marksheet of maths also. Also, a detailed roadmap is also available on the official websites on how to fill the registration form. So you can fill the form easily.


Hope this resolves your query.

Read Complete Answer
Abhishek 12 July,2024
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