Kukurukura nezvemavectors mumasvomhu hakuparadzaniswi nekukurukurirana kweCartesian coordinate system. Cartesian coordinate system ndiyo inonyanya kushandiswa pakugadzira nekuongorora zviitiko zvakasiyana-siyana munzvimbo dzine mativi maviri neatatu. Muchinyorwa chino, tichaongorora pfungwa yemavectors akaenzana muchikamu cheCartesian coordinate system.
Nhanganyaya kumaVectors muCartesian Coordinate System
Muchirongwa cheCartesian coordinate, poindi yega yega iri munzvimbo ine mativi maviri inogona kumiririrwa sepaya yakarongwa (x, y), uko x iri coordinate yakatwasuka uye y iri coordinate yakatwasuka. Kune nzvimbo ine mativi matatu, tine triplet (x, y, z). Vector mune iyi mamiriro ichinhu chemasvomhu chine hukuru (kana hurefu) uye gwara.
Vekitari iri munzvimbo ine mativi maviri inowanzo miririrwa se \(\vec{v}\) = (v_x, v_y), apo \(v_x\) uye \(v_y\) zviri zvikamu zvevekitari iri padivi pe x-axis ne y-axis, zvichiteerana. Munzvimbo ine mativi matatu, vekitari inomiririrwa se \(\vec{v}\) = (v_x, v_y, v_z).
Pfungwa yeVector Equivalence
Mavector maviri anonzi akaenzana kana aine hukuru hwakafanana uye divi rimwe chete, zvisinei nekuti anotangira papi. Mumasvomhu, mavector maviri \(\vec{u}\) = (u_x, u_y) uye \(\vec{v}\) = (v_x, v_y) anonzi akaenzana kana:
1. \(u_x = v_x\)
2. \(u_y = v_y\)
Chaizvoizvo, mavector haana kusungirirwa panzvimbo chaiyo yekutanga. Mavector maviri anogona kuiswa chero kupi zvako muchadenga, asi kana aine divi rimwe chete uye hukuru hwakafanana, achiri kunzi akaenzana, kana kuti akaenzana. Ichi chinhu chakakosha chinoita kuti mavector ave chishandiso chinoshanda zvakanyanya mumasvomhu nefizikisi.
Kufananidza kweJomethri
Ngatitii tine mavector maviri \(\vec{u}\) = (3, 4) uye \(\vec{v}\) = (3, 4). Mavector maviri aya, kana akatariswa muCartesian coordinate system, achamiririra miseve iri munzira imwe chete uye ine hurefu hwakafanana, kunyangwe ichigona kutanga kubva pamapoinzi akasiyana. Saka, kana tikadhirowa \(\vec{u}\) kubva pakutanga (0, 0) kusvika papoindi (3, 4) uye \(\vec{v}\) kubva pakutanga kwakasiyana, ngatitii (1, 1), kusvika papoindi (4, 5), mavector maviri aya achiri akaenzana nekuti ane gwara nehukuru hwakafanana.
Kumiririrwa kweVector Yakaenzana muMasvomhu
Pamasvomhu, mavector akaenzana anotevera musimboti unotevera:
– Kana \(\vec{v}\) = (v_x, v_y) iri vhekitari, saka chero vhekitari yakaenzana ne \(\vec{v}\) inogona kuwanikwa nekuwedzera vhekitari yekushandura yakafanana pakutanga kwayo nepakuguma kwayo.
– Zviri pachena kuti, kana \(\vec{v_1}\) = (v_{1x}, v_{1y}) uye \(\vec{v_2}\) = (v_{2x}, v_{2y}) ari mavector maviri akaenzana, saka pane vector inogara iripo \(\vec{k}\) = (k_x, k_y) zvekuti:
\[
\vec{v_1} = \vec{v_2} + \vec{k} – \vec{k}
\]
Chikamu ichi chinobata munzvimbo ine n-dimensional uye chinosimbisa chokwadi chekuti mavectors anonyanya kutaura nezvekusiyana kwenzvimbo, kwete nzvimbo pachadzo.
Kushandiswa kweMavhitamini Akaenzana muFizikisi
Mufizikisi, pfungwa yemavector akaenzana yakakosha, kunyanya mukuongorora simba, kumhanya, uye momentum. Semuenzaniso, masimba anoshanda panzvimbo yakatarwa muchinhu anogona kushandurwa (seevector akaenzana) kana achiburitsa mhedzisiro imwechete maererano nekumhanya kwakatwasuka kana kuchinja kwemomentum.
Mienzaniso yeMashandisirwo:
1. Masimba Akaenzana uye Mavector Akaenzana:
Mumakanika ekare, kana simba F richimiririrwa sevector uye richishandiswa pane imwe nzvimbo pane chimwe chinhu, tinogona kufambisa nzvimbo yekushandiswa kwesimba nedaro rakaenzana. Izvi zvakakosha pakuverenga nguva dzesimba kana torque, uko zvikamu zvesimba zvakaenzana zvinoshandiswa kugadzirisa matambudziko emakanika.
2. Kumhanya:
Kumhanya sevekita kunoratidza gwara nekumhanya kwekufamba kwechinhu. Semuenzaniso, kumhanya kwemotokari ichifamba kumabvazuva pa60 km/h kunogona kumiririrwa sevekita (60, 0) kana x-axis yakananga kumabvazuva. Vekita dzese dzakaenzana dzinotsanangura mamiriro akafanana ekufamba, kunyangwe nzvimbo dzadzo dzekutanga dzakasiyana, semuenzaniso, (1, 1) kusvika (61, 1).
Makondirakiti Akafanana uye Mavekita Akaenzana
Munzvimbo ine mativi matatu, tinowanzo shandisawo macoordinates akafanana kuti tiwedzere ongororo yedu. Sisitimu iyi inosuma matrix operator projection matrix, iyo inowedzera kunzwisisa kwedu mavectors akafanana. Macoordinates akafanana anowanzo shandiswa mumifananidzo yekombuta kuti zvive nyore kushanduka kwejometri senge kutenderera, kushandura, uye scaling. Mumamiriro ezvinhu aya, mavectors akafanana anotibvumira kuita manipulations akafanana uye akanaka paCartesian coordinates.
Mhedziso
Mavector akaenzana muCartesian coordinate system ipfungwa huru inoumba hwaro hwemashandisirwo akawanda emasvomhu nefizikisi. Kunzwisisa pfungwa iyi kunosanganisira kuziva kuti mavector maviri akaenzana kana aine divi rimwe chete uye hukuru hwakafanana, kunyangwe nzvimbo dzawo dzekutangira dzingave dzakasiyana. Kumiririrwa kwemasvomhu kwemavector akaenzana kunoratidza kuti hunhu uhwu hunobvumira kufambisa nzvimbo dzekutangira nedzekupedzisira dzevector pasina kuchinja hunhu hwavo hwekutanga.
Kushandiswa kwepfungwa iyi muzvikamu zvakasiyana-siyana, zvakaita sefizikisi, kunosimbisa kukosha kwekunzwisisa dzidziso yevector kuti iongororwe zvakanyanya. Munyika chaiyo, pfungwa yemavector akaenzana inobvumira kuverenga zviri nyore kwemasimba, kumhanya, nezvimwe zvinhu zvakawanda zvemakanika uye kinematics.
Nekukwanisa kumiririra nekushandisa mavector muCartesian coordinate system, tinogona kutevedzera nekuongorora mhando dzakasiyana dzezviitiko zvakaoma uye masisitimu zvine mwero wepamusoro wekururama uye kururama. Izvi zvinoita kuti pfungwa yemavector akaenzana ive nyaya inokosha uye inonakidza mukudzidza kwemasvomhu nefizikisi.
