Definition
A vector is a physical quantity that has both magnitude and direction.
The magnitude describes the size of the quantity, while the direction specifies the orientation in which the quantity acts or is measured.
For example, a velocity of 20 m/s east includes both a magnitude (20 m/s) and a direction (east). Both pieces of information are necessary to describe the vector completely.
Magnitude and Direction
The magnitude of a vector is always a non-negative value. It tells us how much of the quantity there is, while the direction tells us where the quantity points or acts.
A direction may be expressed in several ways, including:
- compass directions (north, south, east, west)
- words such as upward, downward, left, or right
- an angle measured from a reference direction
- positive and negative directions along a chosen axis
Examples:
- 5 units upward
- 3 units to the right
- 5 units at 45°
- 4 units in the negative x-direction
The word “units” is used only for illustration. In practice, the magnitude of a vector is expressed using the appropriate unit for the physical quantity being represented, such as meters (m), newtons (N), meters per second (m/s), joules (J), or any other appropriate unit.
Vector Notation
Vectors are usually represented by a letter with an arrow above it.
Examples:
The magnitude of a vector is written using vertical bars.
Examples:
Since magnitude has no direction, it is a scalar quantity.
Examples of Vector Quantities
| Vector Quantity | Description |
| Position | The location of an object relative to a chosen origin. |
| Displacement | The change in an object’s position. |
| Velocity | The rate of change of position. |
| Acceleration | The rate of change of velocity. |
| Force | A push or pull acting in a particular direction. |
| Momentum | The product of an object’s mass and velocity. |
Key Points
- A vector has both magnitude and direction.
- Magnitude describes the size of the vector.
- Direction specifies the orientation of the vector.
- Vectors are represented by a symbol with an arrow above it.
- The magnitude of a vector is written using vertical bars.
- The magnitude of a vector is a scalar quantity.