Physics describes not only how much something happens, but also where and in which direction it happens. This lesson builds the foundation for motion, force, and the laws of mechanics.
Start With a Real-Life Example
Imagine you tell a friend: “I walked 5 kilometers today.” That information is clear: it tells how much.
Now imagine you say: “I walked 5 kilometers towards the east.” Suddenly, the information becomes more complete: it tells how much and in which direction.
This simple difference introduces two important types of physical quantities: scalars and vectors.
Scalar Quantities
A scalar quantity is completely described by magnitude only. It does not need any direction.
Examples
Vector Quantities
A vector quantity needs both magnitude and direction for a complete description.
Examples
Why Is Direction So Important?
Suppose two people push a box:
- One pushes it towards the east.
- The other pushes it towards the west.
Even if both apply the same magnitude of force, the final result depends on the direction. That is why vectors behave very differently from scalars.
Scalar vs Vector: Key Differences
| Feature | Scalar | Vector |
|---|---|---|
| What it needs | Magnitude only | Magnitude + Direction |
| Addition rule | Simple arithmetic addition | Special rules (triangle/parallelogram law, components) |
| Example | Speed = 10 m/s | Velocity = 10 m/s towards east |
| Representation | Ordinary numbers | Arrows (with direction) |
Mathematical Representation (Simple)
- Scalars are represented by ordinary numbers (e.g., 5 kg, 30°C, 12 s).
- Vectors are represented by arrows:
- Length of the arrow → magnitude
- Direction of the arrow → direction
This arrow picture makes it easy to understand why vector addition is different from scalar addition.
Solved Numerical Examples
A person walks 3 km in the morning and 2 km in the evening. Find the total distance covered.
Distance is a scalar, so we add it normally.
A student walks 5 m towards east, then 3 m towards west. Find the net displacement.
Take east as positive (+) and west as negative (−).
So, the net displacement is 2 m towards east.
A person moves 6 m towards east and then 8 m towards north. Find the magnitude of the resultant displacement.
East and north are perpendicular directions, so we use Pythagoras theorem.
Resultant displacement magnitude = 10 m. (Direction would be towards north-east.)
A car travels 120 km in 2 hours. Find its average speed. If the car’s motion is along a straight road towards north, write its average velocity.
Speed is a scalar: 60 km/h.
Velocity is a vector: 60 km/h towards north.
Practice Questions (For Students)
A) Conceptual Questions
- Give 5 examples each of scalar and vector quantities from daily life.
- Why is “10 m” incomplete for displacement but complete for distance?
- Two forces of equal magnitude act on an object in opposite directions. What can you say about the net effect?
- Is speed a scalar or a vector? Explain in one line.
- Can a vector have zero magnitude? Give an example.
B) Numerical Questions
- A person walks 4 km east and 4 km west. Find (i) total distance (ii) net displacement.
- A cyclist moves 12 m north and 5 m east. Find the magnitude of displacement.
- A train travels 180 km in 3 hours. Find average speed.
- An object experiences two forces: 10 N east and 6 N west. Find net force and direction.
- A person walks 10 m east, then 10 m north, then 10 m west. Find the net displacement from the starting point (magnitude and direction).