# Scalar and Vector Quantities  ## Scalar and Vector Quantities:

Physics is an experimental science. We deal with a large number of physical quantities in physics. All physical quantities can be classified into two groups.

• Scalar Quantities.
• Vector Quantities.

## Scalar Quantity:

A physical quantity that is described completely by its magnitude (or size) is called a scalar quantity. A scalar quantity has magnitude only and no direction. Let the mass of a body be 40 kg. We see here that the mass is represented by the number 40 along with the unit kg. This number represents the magnitude or the size of the quantity. So, mass is completely described by magnitude only and is, therefore, a scalar quantity. Length, time, distance, density, volume, area, speed, energy, power, temperature, etc. are all scalar quantities.

## Vector Quantity:

Some physical quantities cannot be described completely by their magnitude. A physical quantity that is described completely by its magnitude (or size) as well as its direction is called a vector quantity. A vector quantity has both magnitude and direction. If a car is moving with a speed of 30 km/h in a particular direction, say north, we say that the velocity of the car is 30 km/h in the North. So, velocity has both magnitude and direction and is, therefore, a vector quantity. Displacement, acceleration, force, torque, weight, momentum, etc. are all vector quantities.

## Representation of Vector:

How do we represent vector quantities on paper? One way to do this would be to write out both the magnitude of the vector and its direction in words. For example, “the velocity of an object is 30 m/s, 30 degrees east of north”. However, such a description can be quite clumsy. A better way of representing vectors is by directed line segments (arrows). The length of the arrow tells us the magnitude of the vector. The direction in which the arrow points gives the direction of the vector. For example, the velocity 30 m/s, 30 degrees east of north is represented by the arrow as shown in the figure. We can choose any convenient scale. If we choose the scale 1 cm = 10 m/s, the length of the arrow would be 3 cm. Similarly, the displacement of 5 km to the west would be represented by an arrow of length 2 cm, if the scale chosen is 2.5 km = 1 cm.