Scalars and Vectors

A scalar quantity has magnitude only (size or numerical value), while a vector quantity has both magnitude and direction.

Force is a vector quantity because it involves both magnitude and direction (e.g., 50 Newtons east).

Volume is a scalar quantity because direction cannot be applied to it (e.g., 50 liters of water).

Vectors can be described by their magnitude and direction (e.g., 100 Newtons at 30 degrees), graphically, or by their x and y components.

Useful equations for vector calculations include the Pythagorean theorem for finding the resultant vector, and trigonometric functions (sine, cosine, arctan) for determining components and angles.

Mass and temperature are scalar quantities as they only have magnitude and cannot be assigned a direction (e.g., 100 grams of aluminum, 90 degrees Fahrenheit).

Distance is a scalar quantity (e.g., 5 miles), while displacement is a vector quantity, as it includes direction (e.g., 5 miles east).

Speed is a scalar quantity (e.g., 30 miles per hour), but velocity is a vector quantity because it specifies direction (e.g., 40 miles per hour north).

Acceleration is a vector quantity because it involves a change in velocity with respect to time, and direction can be applied to it (e.g., accelerating towards the east).