Vektorska metoda u stereometriji

master's thesis

• Author: Ivona Pezelj
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Slaven Kožić (član povjerenstva)
• Committee member: Nikola Sandrić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Na samom početku rada, u prvom poglavlju, obradili smo temeljne pojmove o vektorima i vektorskom računu, definirali usmjerenu dužinu, pojam vektora te pravila za njihovo zbrajanje i množenje istih skalarom. Zatim smo spomenuli pojmove kolinearnosti, komplanarnosti i linearne nezavisnosti vektora koji su potrebni za daljne razumijevanje rada. U narednom poglavlju uveli smo pravokutni Kartezijev koordinatni sustav, definirali radijvektore i podjelu dužine u zadanom omjeru, a formulu za udaljenost dviju točaka izveli vektorski. Također smo definirali ortonormiranu bazu i spomenuli pravila „desne ruke“ i „desnog vijka“. U trećem, četvrtom i petom poglavlju bavili smo se skalarnim, vektorskim i mješovitim produktom vektora. Za svaki smo naveli njihova svojstva pomoću raznih teorema i propozicija, koje smo potom i dokazali, te smo posebno za vektorski i mješoviti produkt prikazali i objasnili njihove geometrijske interpretacije. Na kraju svakog poglavlja riješili smo nekoliko stereometrijskih problema primjenom vektorske metode.

Abstract (english)

At the very beginning of the thesis, in the first chapter, we have dealt with the basic concepts of vectors and vector calculus, defined the directed line segment, concept of vectors and the rules for their addition and multiplication by a scalar. We then mentioned the concept of collinearity, coplanarity and linear independence of vectors which are crucial for further understanding. In the next chapter, we introduced the Cartesian coordinate system, defined the radius vectors, the line segment division in a given ratio and the distance formula is derived using vector method. We also defined the orthonormal basis and mentioned the "right-hand" and "corkscrew" rules. In the third, fourth, and fifth chapters, the scalar, vector, and mixed product of vectors are dealt with. For each of them we specified their properties by means of various theorems and propositions, which we then proved, and in particular for the vector and mixed product we showed and explained their geometric interpretations. At the end of each chapter, we solved several stereometric problems using the vector method.

• Keywords: vektori; vektorski račun; produkt vektora; stereometrijski problemi; rješavanje stereometrijskih problema primjenom vektorske metode
• Keywords (english): vectors; vector calculus; cross product; vector product; stereometric problems; solving stereometric problems using the vector method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:313434
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-02-18 10:33:26