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Definition of vector product
Holý, David ; Halas, Zdeněk (advisor) ; Slavík, Antonín (referee)
Title: Definition of vector product Author: David Holý Department: Department of Mathematics Education Supervisor: Mgr. Zdeněk Halas, DiS., Ph.D., Department of Mathematics Edu- cation Abstract: The main goal of this thesis is to present a compelling and well- motivated definition of the vector product and to explain its properties. Torque serves as a medium through which "the rotating effect of force"is studied on simple physical examples. Elaboration leads to revealing essential properties that define the vector product. The thesis contains the derivation of Cartesian coor- dinates of the vector product. It also contains a list of its basic mathematical properties and applications. Lorentz force is presented as a concrete example of its application and is thoroughly analyzed. In the closing section, the term curl of a vector field is introduced and conceptually explained. The thesis was focused on bringing a good didactic presentation of a vector product, its concrete appli- cations in practice, and its connection to more advanced fields of mathematical inquiry. Keywords: vector product, cross product, torque, Lorentz force, vector field, curl 1
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