Vektorový součin

Abstract

V praci se pokousme naznacit odvozen vektoroveho soucinu postupem zprsnovan podmnek pro vysledny vektor, dokud nen jednoznacne urcen. Prace je psana tak, aby j mel moznost porozumet student stredn skoly, muze tedy slouzit jako inspirace pro ucitele pri vyucovan vektoroveho soucinu na skolach. Nejprve hledame ve 3D vektor kolmy ke dvema linearne nezavislym vektorum. Pote zkoumame, jak vyjadrit obsah rovnobeznku urceneho dvema linearne nezavislymi vektory pomoc souradnic techto vektoru vzhledem ke kar- tezske bazi. Dale naznacujeme, co je orientace vektoroveho prostoru, a mate- maticky ji formalizujeme. Pak uz de nujeme vektorovy soucin a ukazujeme nektere jeho zakladn vlastnosti s tm, ze take ve zkratce naznacujeme, kde se vyuzvaj. 1

In this thesis, we try to indicate a way of obtaining cross product. We use a method of adding conditions de ning a vector, until we are left with the only one that ts them. The text is written in such way that a highschool student should by able to understand it, therefore it can be used as an inspiration for teachers teaching cross product at schools. First, we search for a vector perpendicular to two given linearly independent vectors in 3D. Then we study the area of a parallelogram, which is determined by two linearly independent vectors. Also, we try to express the area using coordinates of these vectors with respect to the cartesian basis. Afterwards, we indicate what an orien- tation of a vector space is and formalize it mathematically. Then we de ne cross product and show some of its basic properties while giving the reader an idea of the eld of their usage. 1