Kuwedzera kwezvikamu zveVectors
Mumasvomhu nefizikisi, mavector ipfungwa huru. Anoshandiswa kutsanangura huwandu hune gwara uye hukuru. Ruzivo rwekuwedzera mavector rwakakosha mumhando dzakasiyana dzesainzi nehunyanzvi. Imwe yenzira dzakajairika dzekuwedzera mavector ndeyekuwedzera kwezvikamu. Chinyorwa chino chichatsanangura misimboti yekutanga yekuwedzera mavector, pfungwa yezvikamu zvevector, uye matanho ekuwedzera mavector nezvikamu.
Chii chinonzi Vector?
Tisati tatanga kuongorora kuwedzera kwevector, tinofanira kunzwisisa kuti vector chii. Vector chinhu chemasvomhu chine hunhu huviri hukuru: hukuru (kana kureba) uye gwara. Muenzaniso wakapfava wevector muhupenyu hwezuva nezuva kufamba kwechinhu. Semuenzaniso, kana mumwe munhu akafamba makiromita mashanu kuchamhembe, tinogona kumiririra rwendo irworwo nevector ine hukuru hwemakiromita mashanu uye gwara rekuchamhembe.
Mavector anowanzo kuratidzwa nemifananidzo semiseve, uko kureba kwemuseve kunoratidza hukuru uye gwara remuseve rinoratidza vector. Mavector anogonawo kuratidzwa sezvikamu zvakafanana ne coordinate axes, zvakaita se x, y, uye z axes mu three-dimensional coordinate system.
Zvikamu zveVector
Vekitari ine zviyero zviviri kana zvitatu inogona kupatsanurwa kuita zvikamu zvinoenderana nema coordinate axes. Semuenzaniso, vekitari ine zviyero zviviri ine kukosha (3, 4) inogona kupatsanurwa seine chikamu che x = 3 uye chikamu che y = 4. Mukutaura kwejometri, izvi zvinoreva kuti vekitari inogona kuonekwa sehuwandu hwemavekitari maviri: vekitari imwe yakafanana ne x-axis ine hukuru hwe 3, uye vekitari imwe yakafanana ne y-axis ine hukuru hwe 4.
Kune vector ine mativi matatu, tine zvikamu zvitatu: x, y, na z. Semuenzaniso, vector (3, 4, 5) ine zvikamu x = 3, y = 4, uye z = 5. MuCartesian coordinate system, vector iyi inogona kumiririrwa semuseve unotangira kubva pakutanga (0, 0, 0) uye uchiguma panzvimbo (3, 4, 5).
Kuwedzera kwezvikamu zveVectors
Iye zvino, tichakurukura maitirwo ekuwedzera mavector uchishandisa nzira ye componentwise. Kuwedzera mavector e componentwise kunosanganisira kuwedzera chikamu chimwe nechimwe chakasiyana. Iyi inzira inoshanda uye inoshanda, kunyanya kana uchishanda nemavector muCartesian coordinate system.
Matanho ekuwedzera maVectors muzvikamu
1. Patsanura vhekitari muzvikamu zvayo:
Danho rekutanga, tinofanira kupatsanura vhekita yega yega kuti iiswe muzvikamu zvayo zvakafanana ne x, y, uye z axes (kana iripo).
2. Kuwedzerwa kwezvikamu zvakafanana:
Pa axis yega yega (x, y, na z), tinowedzera zvikamu zvakafanana. Semuenzaniso, x-component yehuwandu ihuwandu hwezvikamu zvese zve x-zvemavector zviri kuwedzerwa.
3. Batanidza zvakare zvinhu zvakawedzerwa:
Mushure mekunge zvikamu zvese zvawedzerwa, tinosanganisa zvikamu zvakare kuti tiwane sum vector.
Ngatitarisei muenzaniso chaiwo kuti tinyatsojekesa pfungwa iyi.
Muenzaniso wekuwedzera kweVector muzvikamu zviviri
Ngatitii tine mavector maviri muzvikamu zviviri:
– Vekitori A = (3, 4)
– Vekitori B = (1, 2)
Danho 1: Kamura vhekitari yega yega kuita zvikamu zvayo:
– A_x = 3, A_y = 4
– B_x = 1, B_y = 2
Danho rechipiri: Wedzera zvikamu zvakafanana:
- Mhedzisiro yechikamu che x: A_x + B_x = 3 + 1 = 4
– Mhedzisiro yechikamu che y: A_y + B_y = 4 + 2 = 6
Danho rechitatu: Batanidza zvakare zvinhu zvakawedzerwa pamwe chete:
– Vekitori yemhedzisiro = (4, 6)
Saka, mhedzisiro yekuwedzera mavector A naB ivector (4, 6).
Muenzaniso wekuwedzera kweVector muzvikamu zvitatu
Tinogona zvakare kuwedzera muenzaniso uyu kuita mativi matatu. Ngatitii tine mavector maviri mumativi matatu:
– Vekitori C = (2, -1, 3)
– Vekitori D = (1, 4, -2)
Danho 1: Kamura vhekitari yega yega kuita zvikamu zvayo:
– C_x = 2, C_y = -1, C_z = 3
– D_x = 1, D_y = 4, D_z = -2
Danho rechipiri: Wedzera zvikamu zvakafanana:
– Mhedzisiro yechikamu che x: C_x + D_x = 2 + 1 = 3
– Mhedzisiro yechikamu che y: C_y + D_y = -1 + 4 = 3
– Mhedzisiro yechikamu che z: C_z + D_z = 3 – 2 = 1
Danho rechitatu: Batanidza zvakare zvinhu zvakawedzerwa pamwe chete:
– Vekitari yemhedzisiro = (3, 3, 1)
Mugumisiro wekuwedzera mavector C naD ndiyo vector (3, 3, 1).
Kukosha kwekuwedzera kweVector muhupenyu hwezuva nezuva
Kunyangwe kuwedzera mavektori maererano nezvikamu kungaratidzika senyaya inongoitika chete, ine mashandisirwo anoshanda muhupenyu hwezuva nezuva uye munzvimbo dzakasiyana dzehunyanzvi. Mimwe mienzaniso yemashandisirwo inosanganisira:
1. Fizikisi: Pfungwa dzakawanda mufizikisi, dzakadai sesimba, kukurumidza, uye kumhanya, dzinoratidzwa semavekitari. Kuwedzera kwevekitari kunowanzo shandiswa kuverenga simba rinobuda kana kumhanya.
2. Uinjiniya: Muinjiniya, mavector anoshandiswa pakuongorora chimiro, mafambiro emvura, uye electromagnetism. Kuwedzera mavector kunobatsira mainjiniya kugadzira nekuongorora masisitimu akaomarara.
3. Mifananidzo yeKombuta: Mavector anoshandiswa mumifananidzo yekombuta kutsanangura nzvimbo, kumhanya, uye kumhanyisa kwezvinhu. Kuwedzera mavector maererano nezvikamu kwakakosha mukuvandudza mifananidzo uye simulation.
4. Kufamba: Mukufamba, kungave panyika, mugungwa, kana mumhepo, kuwedzerwa kwevector kunoshandiswa kuona nzira nenzvimbo. Tekinoroji yeGPS, semuenzaniso, inoshandisa misimboti yevector kuverenga nzira inoshanda zvakanyanya.
Nekunzwisisa pfungwa huru uye mashandisirwo anoshanda ekuwedzera mavector muzvikamu, tinogona kunzwisisa kukosha kwemavector muzvikamu zvakasiyana-siyana zvehupenyu hwemazuva ano netekinoroji.
Mhedziso
Kuwedzera kwevector yezvikamu inzira inoshanda uye inoshanda yekuwedzera mavector muCartesian coordinate system. Nekupatsanura vector muzvikamu zvayo zvakaenzana ne coordinate axes, tinogona kuwedzera zviri nyore zvikamu izvozvo zvakasiyana tisati tazvibatanidza kuti tiwane vector inobuda. Nzira iyi ine mashandisirwo akawanda anoshanda mufizikisi, engineering, computer graphics, navigation, nezvimwe. Kunzwisisa kuwedzera kwevector yezvikamu hakungosimbisi hwaro hwedu hwemasvomhu nehwepanyama chete asiwo kunovhura mukana wekushandiswa kwakasiyana-siyana kwehunyanzvi nesainzi.
