Scalar and Vector Quantities |Differences & Examples

Scalar and Vector Quantities

A quantity that can be measured is a physical quantity. They are of two types – (i) scalar quantities or scalars, and (ii) vector quantities or vectors. Scalar quantities are those physical quantities that are expressed only by their magnitude, whereas vector quantities require both magnitude and direction to completely express them. Thus, the difference between scalar and vector quantity is the presence of ‘direction’.

In this post, we will learn about scalar and vector quantities with examples and will also try to find out some more differences between the two. To know more about physical quantities visit, my post “Basics of Measurement for Kids“.

SCALAR QUANTITY

Definition of a scalar quantity –

Scalar quantities are those physical quantities which are expressed only by their magnitude along with the unit required for the measurement.

For example – if we say that the mass of a bag is 5.0 kg, it has complete meaning and we are completely expressing the mass of the bag.

Thus, we need the following two parameters to express a scalar quantity, completely :

1. The numerical value of the measured quantity, and
2. The unit in which quantity is being measured.

The numerical value of a scalar quantity along with its unit gives us the magnitude of the quantity. It is always positive.

Examples of scalar quantities

Some of the examples of scalar quantities are – mass, time, length/distance, density, volume, temperature, speed, pressure, energy, power, charge, resistance, mechanical advantage, electric and magnetic potential, angle, etc.

We represent a scalar quantity symbolically by its English letter. For example, ‘m‘ denotes mass, ‘t’ time, ‘d’ distance, ‘s’ speed, etc. Scalar quantities can be added, subtracted, multiplied, and divided by simple mathematic methods.

VECTOR QUANTITY

Definition of a vector quantity –

Vector quantities are those physical quantities which require both magnitude and direction to represent them along with the unit required for the measurement.

For example, – if we say that “displace a stone by 10 m”, the first question that will arise will be “In which direction”?. Here, in this case, without the specification of direction, its meaning is incomplete. But if we say that displace this stone by 10 m towards the north, then it makes complete sense.

Thus, we need the following three parameters to express a vector quantity, completely :

1. the numerical value of the measured quantity,
2. the unit in which quantity is being measured, and
3. the direction of motion.

The numerical value of a vector quantity along with its unit gives us the magnitude of the quantity. The negative sign with a vector quantity implies a reverse or opposite direction. Thus, vector quantities can be positive as well as negative.

Examples of vector quantities

Some of the examples of vector quantities are – displacement, velocity, force, acceleration, electric field, magnetic field, weight, torque, temperature gradient, etc.

A vector quantity is generally written symbolically by its English letter bearing an arrow on it. Sometimes vector quantity is also represented by a bold English letter. For example, ‘d‘ denotes displacement, ‘v‘ velocity, ‘a‘ acceleration, ‘F‘ force, etc. Kindly note, that ‘F‘ and ‘- F‘ are two equal forces acting in opposite directions. We cannot perform simple mathematical operations on vector quantities, unlike scalar quantities. Vector quantities follow different algebra for their addition, subtraction, and multiplication.

DIFFERENCE BETWEEN SCALAR AND VECTOR QUANTITIES

1. Scalar quantities are those physical quantities that are expressed only by their magnitude whereas vector quantities require both magnitude and direction to completely express them.
2. The scalar quantities are always positive whereas vector quantities can be positive as well as negative.
3. A simple mathematical operation can be performed on scalar quantities whereas vector quantities follow complex algebra for their addition, subtraction, and multiplication.

Difference between scalar and vector quantities in tabular form:

S.No.		Scalar Quantity		Vector Quantity
1.		Expressed only by their magnitude		Both magnitude and direction are required to express them
2.		Always positive		Can be positive as well as negative
3.		Scalar quantities can be added, subtracted, multiplied, and divided by simple mathematical methods		Vector quantities require complex algebra to carry out addition, subtraction,  multiplication, and division

Let us understand the difference between scalar and vector quantities in terms of distance and displacement.

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