In this article we show how to apply the method of Galois-graph – one of the means of the formal concept-analysis in order to coordinate the mathematical and didactical requirements. As an example we have chosen the concept of the "vector". As a result of the analysis it is proved that, in elaborating the right vector concept the geometric and algebraic foundations are both needed. The analysis also points out that the geometric model, based on the concept of the "directed segment" is unnecessarily overemphasized in the East-European education.