Scalars and Vectors

Physical quantities come in two fundamental kinds. A scalar has magnitude (size) only, whereas a vector has both magnitude and direction. Distinguishing them and knowing how to combine vectors correctly is essential throughout mechanics, fields, and beyond.

Scalars and vectors compared

Scalar quantities include mass, time, temperature, energy, speed, distance, and electric charge. They are fully specified by a number and a unit; adding them follows ordinary arithmetic. If you walk $3\ \text{km}$ and then $4\ \text{km}$, the total distance is simply $7\ \text{km}$.

Vector quantities include displacement, velocity, acceleration, force, momentum, and electric field strength. They require a direction as well as a magnitude. If you walk $3\ \text{km}$ east and then $4\ \text{km}$ north, your to