Physical quantities are those quantities that can be measured, that is, they describe qualitatively and quantitatively the relationships between the properties observed in the study of physical phenomena.
In Physics, they can be vectors or scalars, such as time, the mass of a body, length, velocity, acceleration, force, and many others. Scalar quantity is one that only needs a numerical value and a unit to determine a physical quantity, an example is our body mass. Quantities such as mass, length, and time are examples of scalar quantities. On the other hand, vector quantities need, for their perfect characterization, a more precise representation. Therefore, they need, in addition to the numerical value, which shows the intensity, a spatial representation that determines the direction and sense. Acceleration, velocity, and force are examples of vector quantities.
Physical quantity is different from physical unit. For example: the Porsche 911 can reach a speed of 300 km/h. In this example, speed is the physical quantity and km/h (kilometers per hour) is the physical unit.
Vector quantities have a special representation. They are represented by a mathematical symbol called a vector. It contains three characteristics of a body or movable, see:
Modulus: represents the numerical value or intensity of the magnitude;
Direction and Sense: determine the orientation of magnitude.
Below we have the representation of any vector quantity and its characteristics, see:
To represent a vector, we take any letter and place an arrow on it, as shown in the figure below:
There are two ways of representing the modulus of a vector. One of them is to have only the letter that represents the vector, without the arrow on top of it. The other form consists of the letter that represents the vector, together with the arrow on it, and between the mathematical signs that represent the module.