A Lesson in the Profiled Preparation in Mathematics in the 11th Grade on the Relation Between the Knowledge of Vectors and Angebraic Equations

With the present work, we would like to share our experience with a generalized lesson on vector operations in the profiled preparation in mathematics in the 11th grade. The purpose of this lesson is to reinforce students’ acquired knowledge by using intra-subject connections between algebra and geometry. The proposed problems for linear and metric operations with vectors are solved by applying some of the before studied properties of functions and methods for solving equations and systems of equations. Problems on linear combinations of vectors, linear dependence and independence, scalar product and perpendicularity of vectors are considered, the solving of which leads to different types of rational, irrational or transcendental equations.