Vector-coordinate method for solving stereometry problems

This manual fully complies with the Federal State Educational Standard (Second generation) The development of skills and skills to solve geometric problems with the vector-coordinate method develops and increases the mathematical culture of students-future students of universities of physico, mathematical and natural-scientific orientation. This book conducts a conversation about the use of vectors and coordinates in solving positions of positional and metric nature in the process of studying such sections of stereometry in grades 10-11, as the geometry of direct and planes, the geometry of polyhedra and rotation figures. At the same time, much attention is paid to the issues of the correct, visual image of spatial figures on the plane and the correct argumentation of statements - problems that arise in the study of stereometry in 10-11 general education classes, classes with in -depth and specialized study of mathematics: these problems are general in nature, regardless of the profile and the use of one or another textbook. Using the images of the correct tetrahedron, cube and the correct hexagonal prism, rotation figures, the methodological recommendations of solving supporting problems, tasks of increased complexity of difficulty on finding distances and angles between straight and planes, calculating the area and volumes of geometric shapes.
Assigned material is selected in compliance with the principle of "from simple - to complex", which allows methodically reasonably implementing the differentiation of training in the solution of geometric problems of various levels of complexity. The thematic set of the tasks of each section is preceded by the reasoned solution of their preparatory set.
answers are indicated to all tasks. Along with the vector-coordinate method, this book proposes solving the problems of the geometry of polyhedra and rotation figures with a synthetic method.
The manual contains lists of the main theorems, formulas of planimetry and stereometry.
The textbook is addressed to students and teachers of mathematics of schools, lyceums, gymnasiums, colleges, as well as undergraduate and graduate students, graduate students, and teachers of pedagogical universities