A geometria analítica com a aplicação de vetores para a resolução de problemas

Abstract

This paper aims to show that the use of vectors in the study of Analytical Geometry in high school has an advantage in not only simplifying the understanding of concepts and demonstrations, but also speeding up problem solving, optimizing time - a very relevant factor in competitions such as the National High School Exam (ENEM). The paper highlights that the vast majority of available mathematics textbooks do not address this subject with the necessary approach, nor do they address it in a vectorial manner. Therefore, this paper can be used by teachers, Olympic students, graduate students, undergraduate students, and those who are aiming for military competitions or who wish to learn more about analytical geometry and vectors. In this dissertation, we have made a historical overview of analytical geometry, from its origins to the present day, we have developed the basic theory of analytical geometry up to straight lines, and the basic study of vectors up to the vector product. For this purpose, we have used the Geogebra software to represent and elucidate some geometric and vector representations in order to fully understand this topic.