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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

Edited By Komal Miglani | Updated on May 07, 2025 05:32 PM IST | #CBSE Class 12th

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
LiveCBSE Result 2025 (LIVE): Class 10, 12 marksheet likely today at cbse.gov.in, Digilocker; websites to checkMay 12, 2025 | 10:32 PM IST

No, the Central Board of Secondary Education is yet to declare CBSE Class 10 results 2025. Once declared, the CBSE 10th result link 2025 will be available on the official website, results.cbse.nic.in.

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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.

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NCERT Solutions Class 12 Maths Chapter 10: Exercise 10.1

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

Answer:

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

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

→OP is displacement vector which |→OP|

= 40 km.

→OP 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∘

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. 10−19coulomb

Answer:

This is a scalar quantity as it has only magnitude.

Question 2 (6): Classify the following measures as scalars and vectors. 20m/s2

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 a→ and vector 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 b→ and Vector 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 a→ and vector c→ have the same magnitude but different direction, they are colinear and not equal.

Question 5: Answer the following as true or false.
(1) a→ and −a→ are collinear.

Answer:

True, a→ and −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.
Background wave

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)

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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Questions related to CBSE Class 12th

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Can I change my board from CBSE to CHSE Odisha in Class 12th?

Changing from the CBSE board to the Odisha CHSE in Class 12 is generally difficult and often not ideal due to differences in syllabi and examination structures. Most boards, including Odisha CHSE , do not recommend switching in the final year of schooling. It is crucial to consult both CBSE and Odisha CHSE authorities for specific policies, but making such a change earlier is advisable to prevent academic complications.

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Manasvini Gupta 30 January,2025
quartely question paper for mathematics cbse

Hello there! Thanks for reaching out to us at Careers360.

Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.

Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!

Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.

If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.

Let me know if you need any other tips for your math prep. Good luck with your studies!

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Jefferson 25 September,2024
i have taken admission in clg after my campartment exam in chemistry along with the neet 2025 preperation but unfortunately i again got campartment after doing all this preparation i got 15 marks only now I can't able to think what should I do next.

It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.

Possible steps:

  1. Re-evaluate Your Study Strategies:

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    • Practice Regularly: Consistent practice is key to mastering chemistry.

  2. Consider Professional Help:

    • Tutoring: A tutor can provide personalized guidance and support.
    • Counseling: If you're feeling overwhelmed or unsure about your path, counseling can help.

  3. Explore Alternative Options:

    • Retake the Exam: If you're confident in your ability to improve, consider retaking the chemistry compartment exam.
    • Change Course: If you're not interested in pursuing chemistry further, explore other academic options that align with your interests.

  4. Focus on NEET 2025 Preparation:

    • Stay Dedicated: Continue your NEET preparation with renewed determination.
    • Utilize Resources: Make use of study materials, online courses, and mock tests.

  5. Seek Support:

    • Talk to Friends and Family: Sharing your feelings can provide comfort and encouragement.
    • Join Study Groups: Collaborating with peers can create a supportive learning environment.

Remember: This is a temporary setback. With the right approach and perseverance, you can overcome this challenge and achieve your goals.

I hope this information helps you.







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Kanishka kaushikii 17 September,2024
i scored 84 percent in cbse 2 years ago.Am i eligible for medhavi scholarship if give 12th again after 2 drop years and will got 75+ in mpboard

Hi,

Qualifications:
Age: As of the last registration date, you must be between the ages of 16 and 40.
Qualification: You must have graduated from an accredited board or at least passed the tenth grade. Higher qualifications are also accepted, such as a diploma, postgraduate degree, graduation, or 11th or 12th grade.
How to Apply:
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Scholarships can range from Rs. 2,000 to Rs. 18,000 per month, depending on the marks obtained and the type of scholarship exam (SAKSHAM, SWABHIMAN, SAMADHAN, etc.).

Since you already have a 12th grade qualification with 84%, you meet the qualification criteria and are eligible to apply for the Medhavi Scholarship exam. Make sure to prepare well for the exam to maximize your chances of receiving a higher scholarship.

Hope you find this useful!

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Yuvan 30 August,2024
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.

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Ashvadha 12 July,2024
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