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

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 vectors. The NCERT chapter Vector Algebra also has the following exercise for practice.

• Vector Algebra Exercise 10.2
• Vector Algebra Exercise 10.3
• Vector Algebra Exercise 10.4
• Vector Algebra Miscellaneous Exercise

Vector Algebra Class 12 Chapter 10 Exercise 10.1

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

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.

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

10Kg

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

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

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

This is a scalar quantity as it has only magnitude.

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

This is a scalar quantity as it has only magnitude.

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

This is a scalar quantity as it has only magnitude.

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

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

This is a scalar quantity as it has only magnitude.

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

(2) distance

Distance is a scalar quantity as it has only magnitude.

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

(3) force

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

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

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

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

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

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.

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.

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.

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.

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 12 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.

Also see-

• NCERT Exemplar Solutions Class 12 Maths Chapter 10
• NCERT Solutions for Class 12 Maths Chapter 10

NCERT Solutions Subject Wise

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• NCERT Solutions for Class 12 Physics
• NCERT Solutions for Class 12 Biology
• NCERT Solutions for Class 12 Mathematics

Subject Wise NCERT Exemplar Solutions

• NCERT Exemplar Class 12 Maths
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