Vector. ukwengeza zithwala

Lolu cwaningo wezibalo kuholela nokunonophala njalo futhi ukwanda ezihlukahlukene lezinto namathuluzi akhombe izenzakalo zemvelo. Ngakho, isandiso umqondo ngokuvumela ukwethula kwebalingisi ambalwa of imvelo, namakilasi entsha lezinombolo yejeyomethri etholwe ukuchaza ezihlukahlukene mafomu. Kodwa ukuthuthukiswa natural sciences kanye mathematics uqobo ucela okudinga isingeniso nokutadisha ezintsha futhi abasafufusa amathuluzi yokumodela. Ikakhulukazi, inani elikhulu tintfo lucobo ayikwazi libhekene kuphela izinombolo, ngoba kubalulekile futhi isiqondiso izenzo zabo. Futhi ngenxa yokuthi kumasegmenti iqondiswe elichaza neziqondiso, amagugu zezinombolo ke, ngenxa yalesi simo futhi uye waphenduka umqondo omusha wezibalo - umqondo we-vector.

Yenza eziyisisekelo imisebenzi zezibalo kubo, futhi, kuchazwe nezizathu ngokomzimba, futhi lokhu okwaholela ekusungulweni Vector-algebra, okuyinto manje ithwala indima enkulu ekwakhiweni eyeza nezazi zezinkanyezi ezikhuluma ngokomzimba. Ngesikhathi esifanayo, izibalo, lolu hlobo algebra futhi ngokuvamile zakhona ziye zaba ulimi elula kakhulu, kanye yokuthola nokubona imiphumela emisha.

Uyini Vector?

Vector iyona iqoqo zonke umugqa izingxenye iqondiswe kokuba nobude obufanayo kanye isiqondiso kusengaphambili. Ngamunye the izingxenye zalesi isethi abizwa ngokuthi Vector izithombe.

Kuyacaca ukuthi vector luchazwa ngegama umfanekiso waso. Zonke izingxenye iqondiswe, amelela a vector, zinobude obulinganako nesiqondiso ababiziweyo, ngokulandelana, ubude (module inani eliphelele) kanye isiqondiso vector. ubude bayo kuboniswa IAI. zithwala ezimbili kuthiwa alingane uma banayo efanayo futhi obulinganako.

umugqa Kuqondiswe ingxenye kabani isiqalo Iphuzu liwukuthi A, futhi ekugcineni - iphuzu B, is ehlukile libhekene i pair ngaphambilini amaphuzu (A B). Cabanga futhi sebuningini ngazimbili (A, A), (B; C) .... Lokhu iqoqo simele Vector othiwa zero futhi okhonjiswe 0. Umfanekiso zero Vector yiliphi iphuzu. Module zero Vector ubhekwa zero. Lo mbono ka-zero Vector isiqondiso akunqunywa.

Uma unanoma yimiphi-zero-non-vector kunqunywa, unikezwa okuphambene, okuyile esesikhundleni obulinganako kodwa kolunye uhlangothi. Zithwala ukuthi babe iziqondiso ezifanayo noma uhlangothi, kuye collinear.

I kungenzeka ngokusebenzisa zithwala elihlobene ne-isingeniso kokusebenza zithwala kanye kudalwa Vector-algebra, okuyinto has izakhiwo eziningi enibaziyo evamile "inombolo" algebra (nakuba Yiqiniso, kukhona umehluko omkhulu).

Ukwengezwa kwe-zithwala ezimbili (collinear) wenziwa umthetho unxantathu (beka umsuka b Vector ekupheleni vector, khona-ke vector a + b uxhuma phezulu Vector a kusukela b Vector ekupheleni) noma parallelogram (ukubeka ekuqaleni zithwala a futhi b ngesinye isikhathi, bese Vector a + b, kokuba ekuqaleni at iphuzu elifanayo, kuyinto diagonal we parallelogram, okuyinto esakhiwe phezu zithwala a futhi b). Ukwengezwa zithwala (ambalwa) engenziwa ngokusebenzisa kokubusa ipholigoni. Uma migomo collinear, ezithintekile ezakhiwe weJiyomethri ziyancipha.

Operations nge zithwala ukuthi kumele bucaciswe izixhumanisi, ziyancipha ukuze imisebenzi ngezinombolo: ukwengeza zithwala - ukwengeza izixhumanisi ezifanele, isb, uma = (x1, Y1) no-b = (x2; y2), ngaleso sikhathi + b = (x1 + X2 ; Y1 + y2).

Ngokuvamile Vector kwalokho has zonke izakhiwo algebraic okuyizinto umuntu azalwa nalo lokuhlaziya kwalokho izinombolo:

1. Ngu permutation isamba engashintshwa:
   a + b = b + i
   Ukwengezwa zithwala nale impahla kulandela ekubuseni parallelogram. Empeleni, yini umehluko ukuthi yini ukuze afingqe zithwala a futhi b, uma diagonal we parallelogram Usenguyena?
2. Impahla associativity:
   (A + b) + c = a + (b + c).
3. Okwenezela kule Vector ye-zero Vector akashintshi yini:
   a +0 = a
   Kusobala ngempela uma sicabange calantsatfu ukwengeza izinto ngombono ofanele.
4. Vector ngasinye has vector okuphambene, okhonjiswe - a; Vector kwalokho, emihle nemibi, kuyoba ilingane no-zero: a + (- a) = 0.