Mavekitari ane mativi maviri muCoordinate System
Pendauluan
Mumasvomhu nefizikisi, mavector ipfungwa inokosha uye anowanzo shandiswa kumiririra huwandu hune hukuru negwara. Mavector ane mativi maviri, kunyanya, mavector ari mundege, anoratidzwa achishandisa zvikamu zviviri zve coordinate. Chinyorwa chino chichapa pfupiso yakadzama yemavector ane mativi maviri mu coordinate system, kusanganisira tsananguro yawo, kumiririrwa, mashandiro ekutanga, uye mashandisirwo muminda yakasiyana-siyana.
Tsanangudzo uye Kumiririrwa
Tsanangudzo yeVekitari
Vector chinhu chine zvinhu zviviri zvakakosha: hukuru negwara. Muhurongwa hwema "two-dimensional" (2D), tinowanzo ratidza ma "vector" se "pairs" akarongwa e "numbers" mbiri.
Kunyora kweVector
Vector \(\mathbf{v}\) mu 2D coordinate system inowanzo tsanangurwa se \(\mathbf{v} = (v_x, v_y)\), apo \(v_x\) uye \(v_y\) zviri zvikamu zvevector pamwe chete ne x- uye y-axes, zvichiteerana. Mune imwe nzira yekunyora, vector inogonawo kunyorwa se \(\mathbf{v} = v_x \mathbf{i} + v_y \mathbf{j}\), apo \(\mathbf{i}\) uye \(\mathbf{j}\) zviri mayuniti vector pamwe chete ne x- uye y-axes, zvichiteerana.
Chinzvimbo Vector
Vector yenzvimbo muenzaniso wakapfava wevector, unoshandiswa zvakanyanya kuratidza nzvimbo yepoindi maererano nekwakabva. Kana poindi A iri pamacoordinates (a, b), saka vector yenzvimbo kubva kwakabva kuenda kupoindi A inonongedzwa se \(\mathbf{A} = (a, b)\).
Kumiririrwa Kwemifananidzo
Vector inogona kuratidzwa semuseve uri mudenga rema coordinate nemuswe wawo uri pamavambo (0, 0) uye muromo wawo uri pamucheto (v_x, v_y). Museve uyu unoratidza kuti poindi iri kure sei uye kuti iri munzira ipi kubva pamavambo.
Mashandiro Ekutanga PamaVectors
Kuwedzera Vector
Kuwedzera mavector maviri kunoitwa nekuwedzera zvikamu zvawo. Semuenzaniso, kana tine mavector maviri \(\mathbf{u} = (u_x, u_y)\) uye \(\mathbf{v} = (v_x, v_y)\), saka kuwedzerwa kwemavector maviri aya ndekwekuti:
\[
\mathbf{u} + \mathbf{v} = (u_x + v_x, u_y + v_y)
\]
Pachitarisiko chejometri, mhedzisiro yekuwedzera uku inogona kuonekwa sekuisa muswe wevector yechipiri pamucheto wevector yekutanga, uye vector yemhedzisiro ivector inobatanidza muswe wevector yekutanga nemucheto wevector yechipiri.
Kubvisa Vector
Kubvisa mavector maviri kwakafanana nekuwedzera, asi zvikamu zvevector zvinobviswa. Kana tiine mavector \(\mathbf{u}\) uye \(\mathbf{v}\) sezvataurwa pamusoro apa, kubvisa ndekwekuti:
\[
\mathbf{u} – \mathbf{v} = (u_x – v_x, u_y – v_y)
\]
Kuwedzera kweScalar
Kuwanda kweScalar ibasa iro vhekitari inowanziridzwa nenhamba (scalar). Kana \(\mathbf{v} = (v_x, v_y)\) uye k iri scalar, saka:
\[
k \mathbf{v} = (k v_x, k v_y)
\]
Chigadzirwa cheDot
Chigadzirwa chedot chemavector maviri \(\mathbf{u}\) uye \(\mathbf{v}\) chinoburitsa scalar uye chakagadzirwa seizvi:
\[
\mathbf{u} \cdot \mathbf{v} = u_x v_x + u_y v_y
\]
Mhedzisiro yekushanda uku inopa ruzivo nezvekuti zvikamu zvemavector maviri aya zviri munzira imwechete zvakadii.
Kureba (Hukuru) hweVector
Kureba kana hukuru hwevector \(\mathbf{v} = (v_x, v_y)\) kunogona kuverengerwa uchishandisa fomura:
\[
|\mathbf{v}| = \sqrt{v_x^2 + v_y^2}
\]
Kureba uku kunomiririra daro kubva pakutanga kusvika panzvimbo (v_x, v_y) mumakotesheni eCartesian.
Mashandisirwo eVector
Fizikisi
Mufizikisi, mavector anowanzo shandiswa kumiririra huwandu hwakasiyana hwemuviri hwakadai sevelocity, acceleration, uye force. Semuenzaniso, kana chinhu chiri kufamba nevelocity isingachinji, inomiririrwa nevector \(\mathbf{v}\), nzira inofambiswa munguva yakatarwa inogona kuverengerwa uchishandisa mavector operations.
Uinjiniya neTekinoroji
Muinjiniya, mavector anoshandiswa pakuongorora zvivako zvisina kusimba uye zvine simba. Semuenzaniso, masimba anoshanda pachivako cheinjiniya anogona kumiririrwa semavector, uye ongororo yacho inoitwa nekupfupisa mavector esimba kuti pawane simba rekudzivirira rinodiwa.
Mifananidzo yeKombuta
Mumifananidzo yemakombiyuta, mavector anoshandiswa kumiririra shanduko dzakasiyana-siyana dzejometri dzakadai sekushandura, kutenderera, uye kukura. Mavector anoshandiswawo mukuvhenekesa nemumvuri kuti aone divi uye simba rechiedza chinorova zvinhu muchikamu che3D.
Zvehupfumi neSainzi yeData
Mukudzidza nezvehupfumi nesainzi yedata, mavector anoshandiswa kakawanda mumhando dzakasiyana dzekuverenga nhamba nedzemuchina. Semuenzaniso, mavector ekuisa zvinhu anoshandiswa mumaalgorithms ekudzidza kwemuchina kufanotaura kana kuisa data muzvikamu.
Mhedziso
Mavector ane mativi maviri zvishandiso zvine simba muzvikamu zvakasiyana-siyana. Kunzwisisa kwekutanga kwekuti mavector anomiririrwa sei uye mashandiro ekutanga anoitwa sei kwakakosha pakushandiswa kwawo. Kubva pafizikisi kusvika kumifananidzo yekombuta, uye kubva kuinjiniya kusvika kusainzi yedata, pfungwa dzevector dzinotibatsira kunzwisisa uye kutevedzera nyika yakatipoteredza nenzira inoshanda uye yakarongeka. Kuziva pfungwa idzi kunovhura mukana wekuwedzera kuongororwa nekuvandudzwa muminda yakasiyana-siyana.
