Vector. Tụkwasị na nke Vektọ

The ọmụmụ nke mgbakọ na mwepụ na-eduga ná a mgbe nile inwetara na-abawanye na dịgasị iche iche nke ihe na ngwá ọrụ maka ịme ngosi uwe gburugburu ebe obibi phenomena. N'ihi ya, ndọtị nke echiche nke ikwe ịme quantitative akparamagwa nke gburugburu ebe obibi, na ọhụrụ na klas nke geometrical ọgụgụ nwetara kọwaa iche iche nke ha iche-iche. Ma mmepe nke eke sayensị na mgbakọ na mwepụ ya choo achọ iwebata na ịmụ ọhụrụ na abụrụ ịme ngosi uwe ngwaọrụ. Karịsịa, a ọnụ ọgụgụ buru ibu nke anụ ahụ quantities nwere ike ghara ji nanị ndị bụ nọmba, n'ihi na ọ dị mkpa na ntụziaka nke omume ha. Ma n'ihi na ndị na-eduzi agba mara na ntụziaka, space ụkpụrụ, mgbe ahụ, a ndabere na-achazi a echiche ọhụrụ banyere mgbakọ na mwepụ - vector echiche.

Igosi isi mgbakọ na mwepụ arụmọrụ na ha, kwa, kọwaa site anụ ahụ na ihe mere, na nke a mesịrị duje na ntọala nke vector algebra, nke ugbu a na-eburu a nnukwu ọrụ ke guzobere ahụ chepụtara. N'otu oge ahụ, na mgbakọ na mwepụ, nke a ụdị algebra na ya generalizations aghọwo a nnọọ adaba asụsụ, nakwa dị ka a n'aka nke inweta na-akọwapụta ọhụrụ pụta.

Gịnị bụ a vector?

Vector bụ set nke niile na-eduzi akara agba ndị nwere otu ogologo na a gaghị agara direction. Onye ọ bụla nke agba nke a set na-akpọ vector oyiyi.

O doro anya na ndị vector na-denoted site onyinyo ya. All eduzi agba, nke na-anọchi anya a vector, bụ otu ogologo na direction nke na-akpọ, karị, ogologo (modul zuru uru) na direction vector. Ogologo ya na-egosi site IAI. Abụọ Vektọ na-sịrị hà ma ọ bụrụ na ha nwere otu direction na otu n'ogologo.

Eduzi akara nke onye mmalite na-ekwu bụ A, na ọgwụgwụ - n'ókè B, na-iche ji ihe nyere iwu ụzọ ihe (A; B). Tụleekwa a plurality nke ụzọ abụọ (A, A), (B; C) .... Nke a set-anọchi anya a vector nke a na-akpọ efu na denoted 0. The oyiyi nke efu vector bụ ọ bụla mgbe. Modul efu vector-atụle ga-efu. Echiche nke efu vector direction na-adịghị kpebisiri ike.

N'ihi na ọ bụla na-abụghị-zero vector kpebisiri ike, nyere ndị na-abụghị, i.e. otu nke nwere otu ogologo ma na-abụghị direction. Vektọ na nwere otu ma ọ bụ na-abụghị ntụziaka, na-akpọ collinear.

Ekwe omume nke na-eji Vektọ metụtara na iwebata arụmọrụ na Vektọ na e kere eke nke vector algebra, nke nwere ọtụtụ Njirimara na-emekarị ndị na-emebu "ọnụ ọgụgụ" algebra (ọ bụ ezie na, n'ezie, e nwekwara ịrịba iche).

Tụkwasị na nke abụọ Vektọ (collinear) a rụrụ site na triangle-achị (ebe mbido nke vector b na ọgwụgwụ nke vector a, mgbe ahụ vector a + b ejikọ n'elu nke vector a si vector ọgwụgwụ b) ma ọ bụ a parallelogram (etinye mmalite Vektọ a na b na otu isi, mgbe ahụ, vector a + b, na-enwe a mmalite n'otu mgbe, bụ a diagonal nke parallelogram, nke na-wuru na Vektọ a na b). Tụkwasị na nke Vektọ (a ole na ole) nwere ike rụrụ site na iji iwu nke polygon. Ọ bụrụ na okwu ndị na-collinear, nwoke geometric rụrụ na-ebelata.

Operations na Vektọ na na-kpọmkwem na-achịkọta, na-ebelata ka arụmọrụ nọmba: mgbakwunye na nke Vektọ - mgbakwunye na nke kwesịrị ekwesị na-achịkọta, e.g., ma ọ bụrụ na a = (x1, y1) na b = (X2; y2), mgbe ahụ, a + b = (x1 + X2 ; y1 + y2).

A vector mgbakwunye nwere niile algebraic Njirimara nke bụ pụta ụwa na mgbakwunye nọmba:

1. Site permutation nchikota na-agbanwebeghị:
   a + b = b + a
   Tụkwasị na nke Vektọ na a onwunwe ndị a si parallelogram achị. N'ezie, ihe dị iche na ihe iji ichikota Vektọ a na b, ma ọ bụrụ na ndị diagonal nke parallelogram ka bụ otu ihe ahụ?
2. The onwunwe nke associativity:
   (A + b) + c = a + (b + c).
3. Na-agbakwụnye na vector nke efu vector adịghị agbanwe ihe ọ bụla:
   a +0 = a
   Ọ bụ nnọọ doro anya ma ọ bụrụ na anyị chere a triangle na mgbakwunye na nke nri anya.
4. Onye ọ bụla vector a nwere ndị na-abụghị vector, denoted site - a; vector adianade do, mma na-adịghị mma, ga-hà efu: a + (- a) = 0.