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## NCERT Class 12 Maths Textbook Chapter 10 With Answer PDF Free Download

### Chapter 10: Vector Algebra

#### 10.1 Introduction

In our day-to-day life, we come across many queries such as – What is your height? How should a football player hit the ball to give a pass to another player on his team?

Observe that a possible answer to the first query may be 1.6 meters, a quantity that involves only one value (magnitude) which is a real number. Such quantities are called scalars.

However, an answer to the second query is a quantity (called force) which involves muscular strength (magnitude) and direction (in which another player is positioned).

Such quantities are called vectors. In mathematics, physics, and engineering, we frequently come across both types of quantities, namely, scalar quantities such as length, mass, time, distance, speed, area, volume, temperature, work, money, voltage, density, resistance, etc. and vector quantities like displacement, velocity, acceleration, force, weight, momentum, electric field intensity, etc.

In this chapter, we will study some of the basic concepts about vectors, various operations on vectors, and their algebraic and geometric properties.

These two types of properties, when considered together give a full realization to the concept of vectors and lead to their vital applicability in various areas as mentioned above.

Author | NCERT |

Language | English |

No. of Pages | 39 |

PDF Size | 4 MB |

Category | Mathematics |

Source/Credits | ncert.nic.in |

### NCERT Solutions Class 12 Maths Chapter 10 Vector Algebra

Question 1:

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

ANSWER:

Here, the vector represents the displacement of 40 km, 30° East of North.

Question 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/s^{2}

ANSWER:

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

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

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

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

(v) 10^{–19} coulomb is a scalar quantity as it involves only magnitude.

(vi) 20 m/s^{2} is a vector quantity as it involves magnitude as well as direction.

Question 3:

Classify the following as scalar and vector quantities.

(i) time period (ii) distance (iii) force

(iv) velocity (v) work done

ANSWER:

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

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

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

(iv) Velocity is a vector quantity as it involves both magnitudes as well as direction.

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

Question 4:

In Figure, identify the following vectors.

(i) Coinitial (ii) Equal (iii) Collinear but not equal

ANSWER:

(i) Vectors and are coinitial because they have the same initial point.

(ii) Vectorsandare equal because they have the same magnitude and direction.

(iii) Vectorsand are collinear but not equal. This is because although they are parallel, their directions are not the same.

Question 5:

Answer the following as true or false.

(i) andare collinear.

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

(iii) Two vectors having same magnitude are collinear.

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

ANSWER:

(i) True.

Vectors andare parallel to the same line.

(ii) False.

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

(iii) False.

It is not necessary for two vectors having the same magnitude to be parallel to the same line.

(iv) False.

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

NCERT Class 12 Maths Textbook Chapter 10 With Answer PDF Free Download