Mavekitari ane mativi matatu muCartesian Coordinate System
Pendauluan
Vector chinhu chemasvomhu chine hukuru uye gwara. Muhupenyu hwezuva nezuva, mavector anowanzo shandiswa kumiririra zviitiko zvakasiyana-siyana zvepanyama zvakaita sekumhanya, simba, uye kutama. Muhurongwa hweCartesian coordinate hune mativi matatu, vector inomiririrwa nezvikamu zvitatu zvine chekuita ne x, y, uye z axes. Chinyorwa chino chichakurukura pfungwa huru dzemavector muhurongwa hweCartesian coordinate hune mativi matatu, mashandiro ekutanga pamavector, uye mamwe emashandisirwo awo anoshanda.
Sisitimu yeCartesian Coordinate ine mativi matatu
Sisitimu yeCartesian coordinate ine mativi matatu ine mativi matatu akatarisana, kureva ma axes e x, y, uye z. Kwakatangira (0,0,0) ndiyo nzvimbo inosangana ma axes matatu aya. Poindi yega yega iri munzvimbo ine mativi matatu inogona kumiririrwa se triplet (x, y, z), apo x iri coordinate iri pa x-axis, y iri coordinate iri pa y-axis, uye z iri coordinate iri pa z-axis.
Kumiririrwa kweVector
Vekitari iri munzvimbo ine mativi matatu inowanzo miririrwa se \(\mathbf{v} = \langle v_x, v_y, v_z \rangle\), apo \(v_x\), \(v_y\), uye \(v_z\) zviri zvikamu zvevekitari iri pamwe chete ne x, y, uye z axes. Semuenzaniso, vekitari \(\mathbf{a} = \langle 3, 4, 5 \rangle\) ine zvikamu \(a_x = 3\), \(a_y = 4\), uye \(a_z = 5\).
Kureba kweVekita
Kureba kana hukuru hwevector \(\mathbf{v}\) hunogona kuverengerwa uchishandisa fomura:
\[ \|\mathbf{v}\| = \sqrt{v_x^2 + v_y^2 + v_z^2} \]
Semuenzaniso, kune vector \(\mathbf{a} = \langle 3, 4, 5 \rangle\), kureba kwacho ndekwekuti:
\[ \|\mathbf{a}\| = \sqrt{3^2 + 4^2 + 5^2} = \sqrt{9 + 16 + 25} = \sqrt{50} = 5\sqrt{2} \]
Mashandiro Ekutanga PamaVectors
Kuwedzera nekubvisa mavector
Kuwedzera mavector maviri kunoitwa nekuwedzera zvikamu zvawo. Kana \(\mathbf{a} = \langle a_x, a_y, a_z \rangle\) uye \(\mathbf{b} = \langle b_x, b_y, b_z \rangle\), saka:
\[ \mathbf{a} + \mathbf{b} = \langle a_x + b_x, a_y + b_y, a_z + b_z \rangle \]
Kusiyana neizvi, kuderedza venhekita kunoitwa nekubvisa zvikamu zvayo:
\[ \mathbf{a} – \mathbf{b} = \langle a_x – b_x, a_y – b_y, a_z – b_z \rangle \]
Kuwedzera kweScalar
Kuwanda kwevector nescalar kunoitwa nekuwanda kwechikamu chimwe nechimwe chevector nescalar. Kana \(k\) iri scalar uye \(\mathbf{a} = \langle a_x, a_y, a_z \rangle\), saka:
\[ k \mathbf{a} = \langle k a_x, k a_y, k a_z \rira \]
Kuwanda kweVector
Chigadzirwa cheDot
Chigadzirwa chedot chemavector maviri chinoburitsa chigadzirwa chescalar uye chinoshandiswa kuverenga kuti mavector maviri akafanana sei. Kana \(\mathbf{a} = \langle a_x, a_y, a_z \rangle\) uye \(\mathbf{b} = \langle b_x, b_y, b_z \rangle\), saka:
\[ \mathbf{a} \cdot \mathbf{b} = a_x b_x + a_y b_y + a_z b_z \]
Chigadzirwa Chinosiyana
Chigadzirwa che mavector maviri chinoburitsa vector itsva yakatarisana nemavector ese ekutanga. Kana \(\mathbf{a} = \langle a_x, a_y, a_z \rangle\) uye \(\mathbf{b} = \langle b_x, b_y, b_z \rangle\), saka:
\[ \mathbf{a} \nguva \mathbf{b} = \langle a_y b_z – a_z b_y, a_z b_x – a_x b_z, a_x b_y – a_y b_x \rangle \]
Mashandisirwo eVectors muhupenyu hwezuva nezuva
Fizikisi
Mufizikisi, mavector anoshandiswa kumiririra huwandu hwakasiyana-siyana, hwakadai sesimba, kumhanya, uye momentum. Semuenzaniso, simba rinokwevera zvinhu rinoshanda pachinhu rinonangidzirwa pakati peNyika uye hukuru hwaro hunoenderana nehuremu hwechinhu uye daro kubva pakati. Tichishandisa mavector, tinogona kuverenga simba rinobuda richishanda pachinhu chinokanganiswa nemasimba akawanda panguva imwe chete.
zvekushandisa
Muinjiniya, mavector anoshandiswa mukuongorora chimiro uye makanika kuti aone masimba anoshanda pachivako kana muchina. Mainjiniya anoshandisa mavector kuti averenge ma torque, stress, uye deformations dzinoitika muzvinhu zvakasiyana mukati mechivako.
Mifananidzo yeKombuta
Mumifananidzo yemakombiyuta, mavector anoshandiswa kumiririra nzvimbo, gwara, uye kufamba kwezvinhu zviri munzvimbo ine mativi matatu. Mavector akakosha pakuchinja kwejometri senge kutenderera, kushandura, uye kukura. Kushandisa mavector kunogona kuita kuti maanimation uye physics simulations zvive zvechokwadi.
Navigation
Mukufamba, mavector anoshandiswa kuona divi uye daro riri pakati penzvimbo mbiri. Masisitimu ekufamba nesatellite akadai seGPS anoshandisa mavector kuverenga nzvimbo uye gwara remotokari kana ngarava. Uchishandisa ruzivo urwu, nzira inokurumidza kana pfupi inogona kuwanikwa.
Mhedziso
Mavector ane mativi matatu muCartesian coordinate system ipfungwa huru inoshandiswa muzvikamu zvakasiyana zvesainzi netekinoroji. Nekunzwisisa hwaro hwemavector, mashandiro ekutanga avanogona kuita, uye mashandisirwo awo muhupenyu hwezuva nezuva, tinogona kushandisa pfungwa iyi kugadzirisa matambudziko akasiyana-siyana anoshanda. Mavector haangorerutsi chete kumiririrwa nekuongorora zviitiko zvepanyama asiwo anovhura nzira yekuvandudza nekuvandudza matekinoroji matsva, akaomarara.
