Galileo distinguished himself from his predecessors by actively attempting to verify his own theories through experimentation and meticulous observation. He combined the results of these experiments with mathematical analysis, pioneering a method that laid the foundation for modern scientific inquiry. Galileo is widely regarded as the world�s first scientist, credited with inventing this scientific approach.Understanding the interplay of both vertical and horizontal motions led Galileo to a profound conclusion. He recognized the need to work with quantities that possess both numerical and directional properties, giving rise to the concept of vectors. Vectors simplify our comprehension of phenomena involving both magnitude and direction, such as displacement, velocity, force, and momentum. In contrast, scalars represent quantities with magnitude but no specific direction, such as temperature or mass. It is important to note that vectors possess their own algebra, including rules for addition, subtraction, and multiplication. However, vector multiplication takes two distinct forms: the dot product and the cross product. While this may initially seem confusing, it is crucial to remember that the outcomes of these multiplications are two different physical quantities, rather than a single unified result as often assumed when dealing with scalars.
Ultimately, the development of vector mathematics and its associated rules emerged from the meticulous observation and understanding of physical phenomena. The scientific community unraveled these concepts by observing the behavior of the natural world and then devised the mathematics to capture and describe these observed phenomena. Therefore, it is essential to recognize that the study of vectors and their rules follows the observation and understanding of physical phenomena, rather than the other way around.