Key Concepts: Scalars vs Vectors

Scalar Quantities

Scalars have only magnitude (size). They are fully described by a number and a unit.

• Examples: mass (5 kg), temperature (300 K), speed (10 m/s), energy (50 J), time (3 s).

Vector Quantities

Vectors have both magnitude and direction. They are represented by arrows.

• Examples: displacement (5 m east), velocity (10 m/s north), force (20 N downward), acceleration (9.8 m/s² down).

Key Differences

• Scalars are added arithmetically: 3 kg + 2 kg = 5 kg.
• Vectors must be added using vector addition (tip-to-tail or component method). Two 3 N forces at right angles give √(9+9) = 3√2 ≈ 4.24 N, not 6 N.
• Distance is a scalar; displacement is a vector. Speed is a scalar; velocity is a vector.