Physic Tutorials

# Scalar And Vector Quantities With Examples [Explained]

Quantities in physics can either be classified as scalars or vectors. These classes of physical quantities are usually handled differently when used in numerical calculations. After this write up you will be able to explain the concept of scalars and vectors and also distinguish between the two quantities.

## What is a scalar quantity?

Many measurable physical quantities we encounter in our study of physics have only numerical values attached to them. Such quantities are completely described when only their magnitudes or sizes are known.

Scalars are defined as physical quantities which have magnitude but no direction associated with them.

Thus a speed of 50kmhr-1 can either be measured in a straight path or a circular path since no direction was indicated. Scalars are added by ordinary algebraic methods.

### Examples of Scalar Quantities

Distance, altitude, speed, mass, time, energy, temperature, potential difference, density, area, work, etc.

## What is a vector quantity?

On the other hand, many other measurable physical quantities have both magnitude or numerical value and also direction as well. Such quantities are not completely described unless their magnitude and directions are specified.

Vectors are defined as physical quantities which have both magnitude and direction. A vector quantity is represented by a line with an arrow on it. The length of the line represents the magnitude while the arrow indicates the direction of the vector.

Thus a displacement is a distance measured in a specified direction, e.g. a bird flies a distance of 100km in a north-easterly direction. Vectors are added by geometrical methods.

### Examples of Vector quantities

Displacement, velocity, acceleration, force, momentum, electric field strength, magnetic field strength, gravitational field strength, etc.

## Questions on Scalar and Vector Quantities

(1) The pair if physical quantities that are scalar only are {UTME 2013}

A. Impulse and time

B. Volume and area

C. Moment and momentum

D. Length and displacement

Solution

Option A: impulse is vector while time is scalar

Option B: volume is scalar, area is scalar

Option C: moment is vector, momentum is vector

Option D: length is scalar, displacement is vector

B is the correct option

(2) Which of the following consists entirely vector quantities? {UTME 2001}

A. Work, pressure and moment                 B. Velocity, magnetic flux and reaction.

C. Displacement, impulse and power.      D. Tension, magnetic flux and mass.

Solution

Vector quantities has both magnitude and direction

Option A – pressure and work are scalar quantities

Option B – they are all vector quantities

Option C- power is a scalar quantity

Option D – mass is a scalar quantity

B is the correct option

### Bolarinwa Olajire

A tutor with demonstrated history of working in the education industry. Skilled in analytical skills. Strong education professional with a M. SC focused in condensed matter.