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The concept of vectors is often difficult for students to grasp and tricky for teachers to tackle in class. Vectors are included in the mathematics and science syllabuses from the second year of general, technological and vocational secondary school. The concept of vectors stems from the intertwined histories of physics and mathematics, but are the same vectors taught in the physical sciences and mathematics in secondary schools? A cross-section of practices and concepts between general and vocational lycées is relevant. As is often the case, a look at history sheds light on and gives meaning to this teaching, and helps to answer the questions: where do vectors and the scalar product come from, and why were they invented?

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