Measurement

Scalar Quantity A physical quantity that has only magnitude (size) and no direction. Examples include mass, temperature, speed, and energy. Scalars obey ordinary arithmetic rules (e.g., 5 kg + 3 kg = 8 kg). In daily life, stating “the temperature is 30 °C” is sufficient; no direction is needed. Vector Quantity A physical quantity that has both magnitude and direction. Examples include displacement, velocity, force, and acceleration. Vectors must be added using geometric or component methods, not simple arithmetic. For instance, walking 5 m east then 5 m north results in a displacement of about 7.07 m northeast, not 10 m. Representation of a Vector A vector is represented by an arrow: length proportional to magnitude, arrowhead indicating direction. In text, a vector is often written in bold (e.g., F) or with an arrow (e.g., F ). The magnitude is written as |F| or simply F . Graphically, the tail is the starting point and the head is the endpoint.