Vectors in Three-Dimensional Space using the Dynamic Mathematics Software GeoGebra
TL;DR
It is demonstrated that the integration of such dynamic models into the educational process intensifies the development of spatial reasoning and increases the level of mastery of stereometry topics.
Abstract
The article is devoted to the theoretical substantiation and practical implementation of a methodology for modeling vectors in three-dimensional space using the dynamic mathematics environment GeoGebra. The paper analyzes the toolset of the environment in the context of operating with stereometric objects and investigates the effectiveness of combining algebraic and graphical approaches to the interpretation of mathematical data. Algorithms for constructing spatial vectors and performing basic linear operations–addition, subtraction, and scalar multiplication – are implemented. Particular attention is paid to the verification of results through the synchronization of analytical computations with their visualization in three-dimensional space, which contributes to a deeper understanding of the geometric nature of vector operations. The practical significance of the study lies in the development of interactive models using the built-in scripting language. This approach enables the automation of computational processes and the creation of an adaptive user interface for conducting experiments with spatial relationships. It is demonstrated that the integration of such dynamic models into the educational process intensifies the development of spatial reasoning and increases the level of mastery of stereometry topics. Prospects for further research are associated with expanding the functional capabilities of the developed model library and integrating more advanced automation algorithms for solving applied problems in geometry.