FUNCIONES VECTORIALES DE ℝm EN ℝn. Funciones Vectoriales de ℝ2 en ℝ y de ℝ3 en ℝ: Operaciones, Límites, Continuidad y Derivabilidad. Derivadas parciales. Funciones reales con dominio en ℝm y rango ℝn. Derivadas. Integrales múltiples. Jacobiano. Máximos y mínimos. Multiplicadores de Lagrange. Aplicaciones de las integrales múltiples en el cálculo de áreas y volúmenes. Didáctica de las funciones vectoriales y la resolución de problemas - Pumapillo Cervantes, Javier Alejandro (2019)
The objective of this research work is to specify that the APOE methodology, the Van Hiele method and the use of the GeoGebra software, combined, should enhance the teaching-learning strategies, facilitating the work of both the teacher and the student. Everything is concentrated in example 2 on page 56, synthesizing, asking for the parametric and symmetric equations of the line that passes through two points A and B located in three-dimensional space, in part b) find the point of intersection of said straight line with plane x y, the latter has a high degree of complexity, the tools that a student must have to face this type of exercises are, obviously, intermediate level algebra as well as the use of trigonometry. Next, I will synthesize the procedures, this will serve as a roadmap which will make explicit what has been worked. First: we obtained the vector equation of the line. Second: From the vector equation of the line, three parametric equations were derived, as a function of "t". Third: By clearing "t" from the three parametric equations, we obtained three symmetric equations. So far we have solved part (a) of the problem, to solve part (b) they ask us to find the point of intersection of the line with the plane y z, for this we must solve the equations and obtain the values ​​of the variables x, y, z contained in the symmetric equations, then the point of intersection will be: (x, y, z)