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VEKTORI . VECTORS

U ĉenik: TAMARA ŠEKULARAC, I razred Matematiĉka gimnazija, Beograd

Mentor: VESNA RAJŠIĆ, profesor matematike Elektro tehniĉka škola „Nikola Tesla”, Beograd

REZIME

Razvoj nauke uslovljavao je postavljanje i rešavanje mnogobrojnih problema u raznim prirodnim naukama,
pa tako i u matematici i fizici. Tokom vekova javljali su se problemi u geometriji, aritmetici i drugim
oblastima matematike i mehanike. Razvojem nauke neke od ovih problema bilo je moguće rešiti. Sloţenost
problema zahtevala je i razvoj matematiĉkih metoda kojima se ti problemi rešavaju. To je dovelo do
proširivanja postojećih i uvodjenja novih pojmova u oblasti mehanike i matematike. Saznanja o vektorima
kao pojmu iz matematike, oblasti linearne algebre, primenjena su prvenstveno da bi se razlikovale veliĉine
koje postoje u prirodi i imaju svoj pravac i smer, i kao takve razlikuju se od nekih drugih veliĉina u prirodi
koje imaju samo svoju veliĉinu i nazivaju se skalari. Vektorima nazivamo veliĉine odredjene sa dva ili više
parametara. Vektori predstavljaju duţi odreĊenog pravca, smera i veliĉine. Njihovo otkriće uticalo je na
rešenja mnogih pitanja u oblasti mehanike i fizike. Razvojem teorije o vektorima omogućeno je rešavanje
realnih problema u raznim oblastima ljudske delatnosti, kako u praktiĉnim tako i u ĉisto teorijskim
zadacima. Vektori se primenjuju u raznim oblastima matematike (geometriji, analitiĉkoj geometriji u
prostoru) i u raznim oblastima istraţivanja u mehanici i fizike. Ideja o ovom istraţivanju o vektorima potekla
je iz ţelje da još jednom ukaţem na karakteristike vektora i njihovu izuzetnu primenu u oblasti metematike i
fizike. Kljuĉne reĉi: vektori, skalarni proizvod, vektorski proizvod, mešoviti proizvod, kordinate vektora,
primena vektora

Summary

Development of science caused stating and solving numerous problems in various natural sciences,
including mathematics and physics. Over the centuries, the problems in geometry, arithmetic and other areas
of mathematics and mechanics emerged. By the development of science it was possible to solve some of
these problems. The complexity of the problems required the development of mathematical methods which
could solve these problems. This led to the expansion and development of new concepts in the field of
mechanics and mathematics. The knowledge about vectors as mathematical concept, the field of linear
algebra, applied primarily to make the distinction between the sizes that exist in nature and have a course
and direction, and as such differ from some other quantities in
nature which have only their own size and are called scalars. The quantities determined by two or more
parameters are called vectors. Vectors represent a straight line of a certain course, direction and size. Their
discovery had an impact on the solution of many issues in the field of mechanics and physics. Development
of the theory of vectors enables solving real problems in various fields of human activity, both in practical as
well as purely theoretical tasks. Vectors are applied in various fields of mathematics (geometry, analytical
geometry in space) and in various areas of research in mechanics and physics. The idea of this research on
vectors derived from my desire to once again bring attention to the characteristics of vectors and their
exceptional application in the field of mathematics and physics.

Key words: vectors, scalar product, vector product, mixed product, vector coordinates, the application of
vectors