• School
  • Engineering and Architecture
  • Management and Business Administration
  • Medicine and Allied Sciences
  • Law
  • Animation and Design
  • Media, Mass Communication and Journalism
  • Finance & Accounts
  • Computer Application and IT
  • Pharmacy
  • Hospitality and Tourism
  • Competition
  • Study Abroad
  • Arts, Commerce & Sciences
  • Learn
  • Online Courses and Certifications
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

Upcoming Event

CBSE Class 12th Exam Date:01 Jan' 26 - 14 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

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

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.

Also Read

JEE Main Highest Scoring Chapters & Topics
Just Study 40% Syllabus and Score upto 100%
Download EBook

Also see-

Recommended eBooks

Related eBooks & Sample Papers

NCERT Solutions Subject Wise

CBSE Class 12th Syllabus: Subjects & Chapters
Select your preferred subject to view the chapters

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

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.

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.

Articles
Related Stories
|
Upcoming School Exams
Mizoram Board of School Education 12th Examination
Ongoing Dates
MBSE HSSLC Application Date

21 Oct'25 - 25 Nov'25 (Online)

Certifications By Top Providers
Weight Management Beyond Balancing Calories
Via Emory University, Atlanta
Modern Building Design
Via University of Bath, Bath
Introduction to Petroleum Engineering
Via Tomsk Polytechnic University, Tomsk
Basic 3D Modeling using Blender
Via Indian Institute of Technology Bombay
Yoga Practices 1
Via Swami Vivekananda Yoga Anusandhana Samsthana, Bangalore
Edx
 1072 courses
Coursera
 816 courses
Udemy
 394 courses
Futurelearn
 265 courses
Explore Top Universities Across Globe
University of Essex, Colchester
Wivenhoe Park Colchester CO4 3SQ
University College London, London
Gower Street, London, WC1E 6BT
The University of Edinburgh, Edinburgh
Old College, South Bridge, Edinburgh, Post Code EH8 9YL
University of Nottingham, Nottingham
University Park, Nottingham NG7 2RD
Bristol Baptist College, Bristol
The Promenade, Clifton Down, Bristol BS8 3NJ

Questions related to CBSE Class 12th

On Question asked by student community

Have a question related to CBSE Class 12th ?
Class 11 English and English grammar syllabus according to half yearly 2025-26 chapter wise

Hello,

You can get the Class 11 English Syllabus 2025-26 from the Careers360 website. This resource also provides details about exam dates, previous year papers, exam paper analysis, exam patterns, preparation tips and many more. you search in this site or you can ask question we will provide you the direct link to your query.

LINK: https://school.careers360.com/boards/cbse/cbse-class-11-english-syllabus

Read Complete Answer
P
Palisetti Rakshita
18 Nov'25
Hello My daughter is in 11th cbse board now and some counselor says we need to change the board to gseb for collages admissions. Is this true that gseb board students will get first preference !? I got mix review. so pls clear the same.

Hello,

No, it’s not true that GSEB (Gujarat Board) students get first preference in college admissions.

Your daughter can continue with CBSE, as all recognized boards CBSE, ICSE, and State Boards (like GSEB) which are equally accepted for college admissions across India.

However, state quota seats in Gujarat colleges (like medical or engineering) may give slight preference to GSEB students for state-level counselling, not for all courses.

So, keep her in CBSE unless she plans to apply only under Gujarat state quota. For national-level exams like JEE or NEET, CBSE is equally valid and widely preferred.

Hope it helps.

Read Complete Answer
S
Sankalp Agrawal
12 Nov'25
Here also provide class 12 cbse board question

Hello,

The Central Board of Secondary Education (CBSE) releases the previous year's question papers for Class 12.

You can download these CBSE Class 12 previous year question papers from this link : CBSE Class 12 previous year question papers (http://CBSE%20Class%2012%20previous%20year%20question%20papers)

Hope it helps !

Read Complete Answer
P
Prachi Kumari
10 Nov'25
12 th commerce public question

Hi dear candidate,

On our official website, you can download the class 12th practice question paper for all the commerce subjects (accountancy, economics, business studies and English) in PDF format with solutions as well.

Kindly refer to the link attached below to download:

CBSE Class 12 Accountancy Question Paper 2025

CBSE Class 12 Economics Sample Paper 2025-26 Out! Download 12th Economics SQP and MS PDF

CBSE Class 12 Business Studies Question Paper 2025

CBSE Class 12 English Sample Papers 2025-26 Out – Download PDF, Marking Scheme

BEST REGARDS

Read Complete Answer
A
Aryan
12 Nov'25
I have passed my 10th and 12th from Delhi, my residency is also in Delhi, I have UP domicile do I participate in both the counselling according to my rank in neet 2nd question is Does i rejected in UP counselling bcoz my address in aadhar is delhi

Hello,

Since you have passed 10th and 12th from Delhi and your residency is Delhi, but your domicile is UP, here’s how NEET counselling works:

1. Counselling Eligibility: For UP NEET counselling, your UP domicile makes you eligible, regardless of where your schooling was. You can participate in UP state counselling according to your NEET rank.

2. Delhi Counselling: For Delhi state quota, usually 10th/12th + residency matters. Since your school and residency are in Delhi, you might also be eligible for Delhi state quota, but it depends on specific state rules.

So, having a Delhi Aadhaar will not automatically reject you in UP counselling as long as you have a UP domicile certificate.

Hope you understand.

Read Complete Answer
S
Sankalp Agrawal
25 Oct'25
View all

Popular CBSE Class 12th Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

 Option 2)

0.16\; J
Option 3)

1.00\; J

 Option 4)

0.67\; J
Read Complete Answer

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

 Option 2)

 6.45×10−3 kg
Option 3)

 9.89×10−3 kg

 Option 4)

12.89×10−3 kg

 
Read Complete Answer

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

 Option 2)

200 \, \, J - 500 \, \, J
Option 3)

2\times 10^{5}J-3\times 10^{5}J

 Option 4)

20,000 \, \, J - 50,000 \, \, J
Read Complete Answer

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

 Option 2)

\; K\;
Option 3)

zero\;

 Option 4)

K/4
Read Complete Answer

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

 Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced
Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

 Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .
Read Complete Answer

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

 Option 2)

3.125 × 10-2
Option 3)

1.25 × 10-2

 Option 4)

2.5 × 10-2
Read Complete Answer

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

 Option 2)

increase two fold
Option 3)

remain unchanged

 Option 4)

be a function of the molecular mass of the substance.
Read Complete Answer

With increase of temperature, which of these changes?

Option 1)

Molality

 Option 2)

Weight fraction of solute
Option 3)

Fraction of solute present in water

 Option 4)

Mole fraction.
Read Complete Answer

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

 Option 2)

6.023 × 1022
Option 3)

half that in 8 g He

 Option 4)

558.5 × 6.023 × 1023
Read Complete Answer

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

 Option 2)

more than 3 but less than 6
Option 3)

more than 6 but less than 9

 Option 4)

more than 9
Read Complete Answer

Applications for Admissions are open.

NEET Most scoring concepts
Get now

This ebook serves as a valuable study guide for NEET 2025 exam.

NEET Previous 10 Year Questions
Get now

This e-book offers NEET PYQ and serves as an indispensable NEET study material.

JEE Main Important Physics formulas
Get now

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

JEE Main Important Chemistry formulas
Get now

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

JEE Main high scoring chapters and topics
Get now

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

JEE Main Important Mathematics Formulas
Get now

As per latest syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

View all Application Forms

CBSE Class 12th Notifications

Latest updates

Never miss an CBSE Class 12th update

Get timely CBSE Class 12th updates directly to your inbox. Stay informed!