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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.

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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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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  • Passing NIOS in October 2024 will make you eligible for NIT admissions in 2025 . NIT admissions are based on your performance in entrance exams like JEE Main, which typically happen in January and April. These exams consider the previous year's Class 12th board results (or equivalent exams like NIOS).

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hello,

Yes you can appear for the compartment paper again since CBSE gives three chances to a candidate to clear his/her exams so you still have two more attempts. However, you can appear for your improvement paper for all subjects but you cannot appear for the ones in which you have failed.

I hope this was helpful!

Good Luck

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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

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

 

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

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

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 .

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

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.

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.

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

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

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