Mashandiro eVector: Pfungwa neMashandisirwo muMasvomhu neSainzi Inoshandiswa
Pendauluan
Chaizvoizvo, vector chinhu chemasvomhu chine hukuru uye gwara. Mavector anowanzo shandiswa kumiririra zviitiko zvakasiyana-siyana musainzi neinjiniya, kusanganisira fizikisi, engineering, uye masvomhu. Muchinyorwa chino, tichakurukura pfungwa huru yemavector, mashandiro anogona kuitwa nawo, uye kuti mashandiro aya anoshandiswa sei muminda yakasiyana-siyana.
Kunzwisisa Mavekta
Muchidimbu, vhekitari inogona kumiririrwa semuseve munzvimbo ine mativi maviri kana matatu. Museve uyu une hurefu hunoenderana nehukuru hwevhekitari, uye gwara rinonongedzera kune imwe nzira. Runyoro rwakajairika rwevhekitari ibhii diki rine museve pamusoro paro kana mabhii matema, akadai se \(\vec{v}\) kana v . Mavhekitari anogona kumiririrwa maererano nezvikamu, semuenzaniso, muzvikamu zviviri, vhekitari \(\vec{v}\) inogona kuratidzwa se \(\vec{v} = v_x \hat{i} + v_y \hat{j}\), apo \(v_x\) uye \(v_y\) zviri zvikamu zve scalar zvevhekitari pamwe chete ne X- ne Y-axes, uye \(\hat{i}\) uye \(\hat{j}\) zviri ma unit vector pamwe chete ne X- ne Y-axes.
Mashandiro Ekutanga PamaVectors
Kuwedzera Vector
Kuwedzera kwevector ndeimwe yemabasa ekutanga anoshandiswa zvakanyanya. Muzvikamu zviviri, kana tine mavector maviri \(\vec{a}\) uye \(\vec{b}\), rimwe nerimwe rine zvikamu \(\vec{a} = a_x \hat{i} + a_y \hat{j}\) uye \(\vec{b} = b_x \hat{i} + b_y \hat{j}\), saka huwandu hwemavector maviri aya ndehwekuti:
\[
\vec{a} + \vec{b} = (a_x + b_x) \hat{i} + (a_y + b_y) \hat{j}
\]
Pachishandiswa geometriki, kuwedzera vheki kunogona kutsanangurwa nenzira ye "musoro-ku-muswe", apo muswe weveki yechipiri unoiswa pamucheto wemusoro weveki yekutanga, uye veki inobuda museve unobatanidza muswe weveki yekutanga nemusoro weveki yechipiri.
Kubvisa Vector
Kubvisa mavector kunoitwa nekuwedzera mavector akapesana. Semuenzaniso, kune mavector \(\vec{a}\) uye \(\vec{b}\), kubvisa \(\vec{a} – \vec{b}\) kwakafanana ne \(\vec{a} + (-\vec{b})\), apo \(-\vec{b}\) iri vector yakatungamirirwa zvakapesana \(\vec{b}\). Mumashoko ezvikamu, izvi zvinoreva:
\[
\vec{a} – \vec{b} = (a_x – b_x) \hat{i} + (a_y – b_y) \hat{j}
\]
Kuwedzera kweScalar
Kuwanda kweScalar ibasa rekuwedzera vhekita ne scalar (nhamba chaiyo). Semuenzaniso, kana \(\vec{v}\) iri vhekita uye \(k\) iri scalar, saka \(k \vec{v}\) ivhekita itsva ine zvikamu \(k v_x \hat{i} + k v_y \hat{j}\). Kuwanda uku kunochinja hurefu (hukuru) hwevekita pasina kuchinja gwara rayo kunze kwekunge \(k\) iri negative, umo inodzosera gwara rayo kumashure.
Chigadzirwa cheDot
Chigadzirwa chedot ibasa riri pakati pemavector maviri rinoita kuti pave nechinhu chinonzi scalar product. Kana tiine mavector maviri \(\vec{a}\) uye \(\vec{b}\), saka chigadzirwa chavo chedot ndeichi:
\[
\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y
\]
Muzvikamu zvitatu, fomura inosanganisira chikamu che z uye inova:
\[
\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y + a_z b_z
\]
Chigadzirwa chedot chinowanzo shandiswa kuverenga kona iri pakati pemavector maviri kana kuona kana mavector maviri ari orthogonal (akatarisana).
Chigadzirwa Chinosiyana
Chigadzirwa chemuchinjikwa ibasa rinongotsanangurwa munzvimbo ine mativi matatu chete uye rinoburitsa imwe vhekita. Kana \(\vec{a}\) uye \(\vec{b}\) ari mavekita maviri ari munzvimbo ine mativi matatu, saka chigadzirwa chavo chemuchinjikwa ndeichi:
\[
\vec{a} \nguva \vec{b} = (a_y b_z – a_z b_y) \hat{i} + (a_z b_x – a_x b_z) \hat{j} + (a_x b_y – a_y b_x) \hat{k}
\]
Vector inobva pachigadzirwa chakasiyana yakatarisana nemavector ekutanga uye kutungamira kwayo kunotsanangurwa nemutemo wekurudyi.
Mashandisirwo Ekushanda kweVector
Fizikisi neUinjiniya
Mufizikisi, mavector anoshandiswa kumiririra huwandu hwakasiyana-siyana, hwakadai sekumhanya, kukurumidza, uye simba. Kuwedzera nekubvisa mavector kwakajairika mukuongorora kufamba uye dynamics. Semuenzaniso, simba rese rinoshanda pachinhu ihuwandu hwevector hwemasimba ese anoshandiswa kuchinhu ichocho.
Chigadzirwa chedoti chinowanzo shandiswa mu electrodynamics kuverenga basa rinoitwa nesimba, nepo chigadzirwa chemuchinjikwa chinowanzo shandiswa mumakanika kuverenga nguva yesimba kana torque.
Mifananidzo yeKombuta
Mumifananidzo yemakombiyuta, mavector akakosha pakuchinja kwejometri, senge kutenderera, kukura, uye kushandura zvinhu. Matekiniki ekuchinja anowanzo shandiswa pamwe chete nekushanda kwevector kushandura nzvimbo uye kurongeka kwezvinhu munzvimbo ine mativi matatu.
Kuongorora Data uye Kudzidzira Kwemichina
Mukuongorora data uye kudzidza kwemuchina, mavector anoshandiswa kumiririra data. Mavector emhando yepamusoro imhando yedata inogonesa maalgorithms kuona mapatani uye kufanotaura. Mashandiro evector, akadai sekuwedzera uye kuwedzera scalar, anoshandiswa kakawanda mukugadzirisa maalgorithms uye matekiniki ekudzidza zvakadzama.
Kuenzanisa Kwemari
Muhupfumi nezvemari, mavector anoshandiswa mukugadzira mapotefolio kumiririra musanganiswa wemidziyo yakasiyana. Mabasa evector anobatsira pakuverenga njodzi yepotefolio nekudzoka kwayo uye mukushandura midziyo kuti iwedzere kudzoka kwayo uye kuderedza njodzi.
Mhedziso
Mashandiro eVector anoita basa rakakosha muzvikamu zvakasiyana zvesainzi neinjiniya. Anopa maturusi ane simba ekuongorora nekugadzira zvinhu zvine chekuita nehuwandu negwara. Nekunzwisisa mashandiro ekutanga akadai sekuwedzera, kubvisa, kuwanda kwe scalar, chigadzirwa chemadot, uye chigadzirwa chakayambuka, tinogona kushandisa pfungwa idzi mumhando dzakasiyana dzemashandisirwo, kubva kufizikisi kusvika pakudzidza kwemuchina. MaVector haasi maturusi emasvomhu chete asiwo bhiriji rinobatanidza dzidziso nekushandiswa kwenyika chaiyo, zvichitigonesa kunzwisisa nyika zviri nani uye kuita sarudzo dziri nani zvichibva pakuongorora kwakanyatsojeka.
