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

## NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.1 – CBSE Free PDF Download

Exercise 10.1 of NCERT Solutions for Class 12 Maths Chapter 10 – Vector Algebra is based on the following topics:

1. Introduction
2. Basic Concepts
• Position Vector
• Direction Cosines

Solving the problems of Exercise 10.1 will help the students understand the topics mentioned above in a better way.

## Download the PDF of NCERT Solutions for Class 12 Maths Chapter 10 – Vector Algebra Exercise 10.1

### Access Answers to NCERT Solutions Class 12 Maths Chapter 10 – Vector Algebra Exercise 10.1 Page Number 428  ### Access Other Exercises of Class 12 Maths Chapter 10

Exercise 10.2 Solutions 19 Questions

Exercise 10.3 Solutions 18 Questions

Exercise 10.4 Solutions 12 Questions

Miscellaneous Exercise Chapter 10 Solutions 19 Questions

#### Access Answers to NCERT Class 12 Maths Chapter 10 – Vector Algebra

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

Solution: The vector represents the displacement of 40 km, 30o east of north.

2. Classify the following measures as scalars and vectors.

(i) 10 kg

(ii) 2 metres north-west

(iii) 40°

(iv) 40 watt

(v) 10–19 coulomb

(vi) 20 m/s2

Solution:

(i) 10 kg is a scalar quantity because it has only magnitude.

(ii) 2 meters north-west is a vector quantity as it has both magnitude and direction.

(iii) 40° is a scalar quantity as it has only magnitude.

(iv) 40 watts is a scalar quantity as it has only magnitude.

(v) 10–19 coulomb is a scalar quantity as it has only magnitude.

(vi) 20 m/s2 is a vector quantity as it has both magnitude and direction.

3. Classify the following as scalar and vector quantities.

(i) time period

(ii) distance

(iii) force

(iv) velocity

(v) work done

Solution:

(i) Time period is a scalar quantity as it has only magnitude.

(ii) Distance is a scalar quantity as it has only magnitude.

(iii) Force is a vector quantity as it has both magnitude and direction.

(iv) Velocity is a vector quantity as it has both magnitude and direction.

(v) Work done is a scalar quantity as it has only magnitude.

4. In the figure, identify the following vectors: (i) Coinitial

(ii) Equal

(iii) Collinear but not equal

Solution: directions are not the same.

5. Answer the following (True or False).

(i) and are collinear.

(ii) Two collinear vectors are always equal in magnitude.

(iii) Two vectors having the same magnitude are collinear.

(iv) Two collinear vectors having the same magnitude are equal.

Solution:

(i) True

Vectors and are parallel to the same line.

(ii) False

Collinear vectors are those vectors that are parallel to the same line.

(iii) False

Two vectors having the same magnitude need not necessarily be parallel to the same line.

(iv) False

Only if the magnitude and direction of two vectors are the same, regardless of the positions of their initial points the two vectors are said to be equal.

Types of Vectors

• Zero Vector
• Unit Vector
• Coinitial Vectors
• Collinear Vectors
• Equal Vectors
• Negative of a Vector