| Definition | Quantities that have only magnitude. | Quantities that have both magnitude and direction. |
| Examples | Speed, distance, mass, time, temperature, energy, work. | Velocity, displacement, force, acceleration, momentum. |
| Representation | A single numerical value (e.g., 50 km). | Represented as arrows or with unit vectors (e.g., 50 km east). |
| Direction | No direction involved. | Always associated with a specific direction. |
| Addition Rules | Follows simple arithmetic addition. | Requires vector addition using head-to-tail rule or components. |
| Physical Interpretation | Describes “how much” or “quantity”. | Describes “how much” and “in which direction”. |
| Negative Values | Cannot inherently indicate direction. | Can indicate direction through negative values (e.g., -5 m/s). |
| Measurement Units | Depends on the type of quantity, e.g., meters, seconds. | Similar units but accompanied by direction, e.g., 5 m north. |
| Mathematical Expression | Treated as simple numbers. | Represented as vectors (e.g., v = 5î + 3ĵ). |
| Example in Motion | Speed (e.g., 60 km/h). | Velocity (e.g., 60 km/h north). |
| Example in Energy | Energy (e.g., 50 joules). | Force (e.g., 10 N downward). |
| Complexity | Easier to handle computationally. | Requires additional mathematical tools (e.g., trigonometry). |
