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

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

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CBSE Class 12th Exam Date:17 Feb' 26 - 17 Feb' 26

#CBSE Class 12th
Komal MiglaniUpdated on 07 May 2025, 05:32 PM IST

Imagine you are flying a drone it is not enough to say it moved 5 meters; you also need to know where it went (like north or upward). That is exactly what vectors help with In Class 12 maths exercise 10.1 solutions, you will learn how to represent such directional movements, which are useful in fields like navigation, physics, and engineering. This is an important chapter for both board exams and competitive exam like JEE ,NEET etc.

NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1 is not just for boards; it also builds a strong base for JEE Main and even helps with NEET Physics topics involving vectors. This NCERT solution for Class 12 Maths step-by-step solutions are made by faculty experts to match student needs, making complex problems easier to understand. Regular practice boosts your concept clarity, speed, and confidence.

This Story also Contains

  1. Class 12 Maths Chapter 10 Exercise 10.1 Solutions: Download PDF
  2. NCERT Solutions Class 12 Maths Chapter 10: Exercise 10.1
  3. Topics Covered in Chapter 10 Vector Algebra: Exercise 10.1
  4. NCERT Solutions Subject Wise
  5. Subject Wise NCERT Exemplar Solutions

Class 12 Maths Chapter 10 Exercise 10.1 Solutions: Download PDF

Download the PDF of Class 12 Maths Chapter 10 Exercise 10.1 solutions of NCERT for easy, offline revision anytime, anywhere. NCERT solution for Class 12 is super helpful for building a strong base in vectors and great for both board exams and JEE prep.

Download PDF

NCERT Solutions Class 12 Maths Chapter 10: Exercise 10.1

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

Answer:

Represent graphically a displacement of 40 km, $30 ^\circ$ 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. $40 ^\circ$

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

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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

Screenshot%20Capture%20-%202025-04-29%20-%2013-47-50

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

Screenshot%20Capture%20-%202025-04-29%20-%2013-47-50

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 collinear vectors with the same magnitude can have opposite direction

Topics Covered in Chapter 10 Vector Algebra: Exercise 10.1

Some Basic Concepts

  • Position Vector: It indicates the location of a point in space in terms of the origin.
  • Direction Cosines: These are the cosines of the angles a vector makes with the x, y, and z axes.

Types of Vectors

  • Zero Vector: A vector with zero length and no definite direction.
  • Unit Vector:A vector of unit magnitude, representing direction alone.
  • Coinitial Vectors: Vectors which have the same initial point.
  • Collinear Vectors: Vectors that are along the same line or parallel lines.
  • Equal Vectors: Vectors of the same magnitude and direction, but no regard for starting point.
  • Negative of a Vector: A vector of the same magnitude but opposite direction.

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NCERT Solutions Subject Wise

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Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

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

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.

Q: How to identify that the given vectors are equal?
A:

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

Q: Can two collinear vectors have different directions?
A:

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

Q: Is it a necessary condition for collinear vectors to have the same magnitude?
A:

No, collinear vectors can have different magnitudes.

Q: 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?
A:

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

Q: Is power a vector quantity?
A:

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

Q: What questions are expected for exams from Class 12 Maths chapter 10 exercise 10.1?
A:

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

Q: What does the initial question of exercise 10.1 Class 12 Maths signify?
A:

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.

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English ka mid term question 2025-26

Here is Link you can refer: https://school.careers360.com/download/ebooks/karnataka-sslc-mid-term-english-answer-key-2025-26

Also,

check your school website or notice board regularly for any updates about the English mid-term exam question paper for 2025–26. The school usually uploads or announces it before the exam schedule.

Next, focus on revising all chapters from the first half of the syllabus. Practice grammar rules, comprehension passages, and essay writing to strengthen your basics and writing skills.

Finally, keep your admit card, timetable, and stationery ready before the exam. Stay calm, manage your time well, and revise once more before the test day for better results.

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Vanshika Saini
26 Oct'25
12th Exam 2025Kitin tareekh ko hoga

Hello,

The date of 12 exam is depends on which board you belongs to . You should check the exact date of your exam by visiting the official website of your respective board.

Hope this information is useful to you.

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21 Sep'25
12th biology question paper 2023-2025

Hello,

Class 12 biology questions papers 2023-2025 are available on cbseacademic.nic.in , and other educational website. You can download PDFs of questions papers with solution for practice. For state boards, visit the official board site or trusted education portal.

Hope this information is useful to you.

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Nidhi Raghuwanshi
21 Sep'25
In March 2025, I passed the CBSE 12th board and gave KCET. I am taking a drop year. I will reappear in the CBSE board exam in the upcoming 2026 exam in February as a private candidate to increase my PCM aggregate, as KCET gives 50% weightage to PCM aggregate, and I will also give the KCET exam. So, to calculate rank, do they use the board marksheet from 2025 or 2026? Also for each subject will best out of two marks accross both the marksheets be considered? #kcet

Hello Pruthvi,

Taking a drop year to reappear for the Karnataka Common Entrance Test (KCET) is a well-defined process. As a repeater, you are fully eligible to take the exam again to improve your score and secure a better rank for admissions.

The main procedure involves submitting a new application for the KCET through the official Karnataka Examinations Authority (KEA) website when registrations open for the next academic session. You must pay the required application fee and complete all formalities just like any other candidate. A significant advantage for you is that you do not need to retake your 12th board exams. Your previously secured board marks in the qualifying subjects will be used again. Your new KCET rank will be calculated by combining these existing board marks with your new score from the KCET exam. Therefore, your entire focus during this year should be on preparing thoroughly for the KCET to achieve a higher score.

For more details about the KCET Exam preparation, CLICK HERE.

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

Thank you, and I wish you all the best in your bright future.

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Ark Pandey
20 Sep'25
I'm studying scince in karnatakastate board, can i take commerce in cbse for 12th next year?

Yes, you can switch from Science in Karnataka State Board to Commerce in CBSE for 12th. You will need a Transfer Certificate from your current school and meet the CBSE school’s admission requirements. Since you haven’t studied Commerce subjects like Accountancy, Economics, and Business Studies, you may need to catch up before or during 12th. Not all CBSE schools accept direct admission to 12th from another board, so some may ask you to join Class 11 first. Make sure to check the school’s rules and plan your subject preparation.



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