In the more difficult subjects in school, a common question you might hear students ask is “Why do I need to learn this?“, and “when are we going to use this in life anyway?” Vectors are one of these subjects. So, this essay is written to clarify that us humans do, every once in awhile, use vectors in our lives. The content of this essay will include who created vectors, which occupations use vectors, how vectors relate to other subjects in math, and more intriguing ideas.
(No, not Vector from Despicable Me.)
A vector is a quantity that has a direction and magnitude. Vectors can be graphed on a coordinate plane with its terminal and initial point, or on the coordinate plane with its component vector. They can create triangles, by drawing the opposite side and adjacent side of the direction angle of the vector together. Ideas of vectors originated
Long before history had been recorded, the parallelogram law for addition of vectors was seen in Aristotle’s work B.C, and Isaac Newton in the 1700s. In 1827, August Ferdinand Möbius published a book by the name of “The Barycentric Calculus”. In it, he introduced line segments that had a direction. He labeled them with letters of the alphabet. These later became known as vectors.
While Möbius was a mathematician, his job is not the only one that uses vectors today. Chemical engineers, actuaries, software engineers, agricultural engineers, machinists, and meteorologists are few of the numerous occupations. Chemical engineers use vectors to calculate kinetic energy, measure the concentration of buffers (solutions that can maintain a nearly constant pH if it is diluted), and process data. Meteorologists use vectors when predicting weather patterns.
“But I don’t want any those jobs when I get older,” students may proclaim. Vectors are still important to learn because they relate to other ideas in math. Vectors are applications of trigonometry, they can be seen as the hypotenuse of a right triangle. Vectors use the Law of Sine to find degrees and angles when two lengths, and an opposing angle, or two angles and an opposing length of the triangle the vector makes are known. Law of Cosine is used to find a length of a triangle that has two lengths given, and an angle that is opposing the missing length.
There is still much more research to be done on why vectors are important. There are many more occupations that use vectors, and they relate to many different units in math. In summary, while the ideas of vectors were around long before the 1800s, Möbius was the first to truly capture its definition. Vectors today are used in many occupations, and relate to other ideas in math, including the Laws of Sine and Cosine. From the information presented in this essay students, like myself, may now be at ease when learning about vectors and any other questionable math subjects to come.