Scalars are physical quantities which have only a number value or a size (magnitude). A scalar tells you how much of something there is.
DEFINITION
Scalar
A scalar is a physical quantity that has only a magnitude (size).
For example, a person buys a tub of margarine which is labelled with a mass of
500
500
g
g
. The mass of the tub of margarine is a scalar quantity. It only needs one number to describe it, in this case,
500
500
g
g
.
Vectors are different because they are physical quantities which have a size and a direction. A vector tells you how much of something there is and which direction it is in.
DEFINITION
Vector
A vector is a physical quantity that has both a magnitude and a direction.
For example, a car is travelling east along a freeway at
100
100
km⋅h−1
km·h−1
. What we have here is a vector called the velocity. The car is moving at
100
100
km⋅h−1
km·h−1
(this is the magnitude) and we know where it is going – east (this is the direction). These two quantities, the speed and direction of the car, (a magnitude and a direction) together form a vector we call velocity.
Examples of scalar quantities:
mass has only a value, no direction
electric charge has only a value, no direction
Examples of vector quantities:
force has a value and a direction. You push or pull something with some strength (magnitude) in a particular direction
weight has a value and a direction. Your weight is proportional to your mass (magnitude) and is always in the direction towards the centre of the earth.