Vector. Bugu da kari na vectors

A nazarin ilmin lissafi take kaiwa zuwa wani m enrichment da wani karuwa a iri-iri na abubuwa da kuma kayayyakin aiki, don yin tallan kayan kawa muhalli mamaki. Saboda haka, tsawo daga cikin manufar kyale gabatar gwada yawa faye hali na yanayi, tare da sabon azuzuwan na geometrical Figures samu don bayyana iri-iri na da siffofin. Amma ci gaban kimiyyar yanayin halitta da kuma lissafi kanta buƙatun bukatar gabatarwar da kuma nazarin sabon da kuma kunno kai tallan kayan kawa da kayayyakin aiki. A musamman, babban adadin na jiki yawa ba za a iya halin ne kawai da lambobi, domin shi ne mai muhimmanci da kuma shugabanci na ayyukansu. Kuma saboda directed segments faye hali da kuma kwatance, da lamba dabi'u, sa'an nan, a kan wannan hasashe kuma ya juya wani sabon ra'ayi na lissafi - vector ra'ayi.

Yi asali ilmin lissafi aiki a kan su, kuma, a tsare ta jiki dalilai, kuma wannan yana yiwuwa ya haifar da kafa vector aljabara, wanda yanzu daukawa mai babbar rawar a cikin samuwar jiki theories. A daidai wannan lokaci, a cikin lissafi, wannan irin aljabara kuma ta generalizations sun zama sosai dace harshe, kazalika da wajen samun kuma gano sabon sakamako.

Mene ne wani vector?

Vector ne sa na duk directed line segments da ciwon guda tsawon da qaddara shugabanci. Kowace daga cikin segments na wannan sa aka kira vector images.

A fili yake cewa vector aka denoted da ta image. All directed segments, wanda wakiltar wani vector, iri daya ne tsawon da shugabanci wanda ake kira, daidai da, da tsawon (module cikakkar darajar) da kuma shugabanci vector. Its tsawon aka nuna ta IAI. Biyu vectors an ce daidai idan suna da wannan shugabanci da kuma guda tsawon.

Directed line kashi wanda farawa ne A, da kuma karshen - batun da B, an uniquely halin da umurni biyu daga maki (A; B). La'akari kuma da wani jam'i na nau'i-nau'i (A, A), (B; C) .... Wannan sa wakiltar wani vector wanda ake kira sifili da denoted 0. Hoton na da sifili vector ne wani batu. Module sifili vector aka dauke su sifili. Wannan mas'ala ta sifili vector shugabanci ba niyya.

Ga wani maras sifili vector aka ƙaddara, ba akasin, cewa shi ne, daya cewa yana da wannan tsawon, amma a gaban shugabanci. Vectors da cewa suna da wannan ko gaban kwatance, da ake kira collinear.

Da yiwuwar amfani da vectors hade da gabatarwar aiki a kan vectors da halittar vector aljabara, wanda yana da yawa Properties a na kowa tare da saba "lamba" aljabara (ko da yake, ba shakka, akwai kuma gagarumin bambance-bambance).

Bugu da kari na biyu vectors (collinear) da aka yi da alwatika mulki (sanya asalin vector b a ƙarshen vector wani, sa'an nan da vector wani + b haɗu da saman vector wani daga vector karshen b) ko wani parallelogram (sa fara vectors a kuma b a daya batu, sa'an nan vector wani + b, ciwon farkon a wannan aya, shi ne a diagonal na parallelogram, wanda aka gina a kan vectors a kuma b). Bugu da kari na vectors ( 'yan) za a iya yi ta amfani da mulki na polygon. Idan sharuddan ne collinear, Game da lissafi constructions an rage.

Ayyuka da vectors, wanda sets da tsarawa an rage wa ayyukan da lambobi: Bugu da kari na vectors - Bugu da kari daga cikin jerin tsarawa, misali, idan wani = (x1. Y1) da kuma b = (x2, y2), sa'an nan a + b = (x1 + x2 ; y1 + y2).

Yawanci vector Bugu da kari yana da dukan algebraic Properties wanda ne muhimmi ga Bugu da kari lambobi:

1. By permutation ware Naira Miliyan Xari da aka canza ba:
   mai + b = b + wani
   Bugu da kari na vectors tare da wannan dukiya ya zama mulkin parallelogram. Lalle ne, abin da shi ne bambanci a abin domin takaita vectors a kuma b, idan diagonal na parallelogram ne har yanzu wannan?
2. Dũkiyar associativity:
   (A + b) + c = wani + (b + c).
3. Ƙara zuwa vector na sifili vector bai sauya ba wani abu:
   wani +0 = a
   Yana da quite na fili idan muka kwatanta alwatika da Bugu da kari na dama hangen zaman gaba.
4. Kowane vector wani yana da m vector, denoted ta - a. vector Bugu da kari, tabbatacce kuma korau, zai zama daidai da sifili: wani + (- a) = 0.