Kubvisa Vector: Zvinokosha, Mitemo, uye Mashandisirwo
Kubvisa mavector ipfungwa huru mumasvomhu, fizikisi, uye mainjiniya. Muhupenyu hwezuva nezuva, tinowanzo sangana nemamiriro ezvinhu apo tinoda kubvisa mavector maviri kana anopfuura, semuenzaniso pakuverenga mafambiro emhepo kana kufamba kwezvinhu. Chinyorwa chino chichakurukura nezvekuderedza mavector zvakadzama, kusanganisira tsananguro yayo, misimboti yekutanga, mitemo, uye mashandisirwo ayo muminda yakasiyana-siyana.
Tsanangudzo yeVekitari
Vector huwandu hune hukuru (kana kureba) uye gwara. Mienzaniso yevector inosanganisira kumhanya, kukurumidza, simba, uye simba remagetsi. Vectors dzinowanzo miririrwa semiseve pamadhayagiramu, uko kureba kwemuseve kunoratidza hukuru uye gwara remuseve rinoratidza gwara rehuwandu.
Panyaya yemasvomhu, mavector ari muzvikamu zviviri anowanzo nyorwa muchimiro che \( \mathbf{a} = (a_1, a_2) \) kana muchimiro chenguva dzose \( \mathbf{a} = ai + bj \), apo \( i \) uye \( j \) ari mavector eyuniti mugwara re x- ne y.
Kubvisa Vector: Pfungwa Dzekutanga
Kubvisa mavector ndiko kushanda kwekuwedzera mavector asina kunaka. Kana tiine mavector maviri \( \mathbf{a} \) uye \( \mathbf{b} \), saka kubvisa \( \mathbf{a} – \mathbf{b} \) kwakafanana ne \( \mathbf{a} + (-\mathbf{b}) \). Vector isina kunaka yevector \( \mathbf{b} \) ivector ine hukuru hwakafanana asi yakapesana.
Pamasvomhu, kana \( \mathbf{a} = (a_1, a_2) \) uye \( \mathbf{b} = (b_1, b_2) \), saka:
\[ \mathbf{a} – \mathbf{b} = (a_1, a_2) – (b_1, b_2) = (a_1 – b_1, a_2 – b_2) \]
Muenzaniso wekubvisa mavector muzvikamu zviviri
Ngatitii tine mavector maviri muzvikamu zviviri, \( \mathbf{a} = (4, 3) \) uye \( \mathbf{b} = (1, 2) \). Kubvisa mavector maviri aya ndekwekuti:
\[ \mathbf{a} – \mathbf{b} = (4 – 1, 3 – 2) = (3, 1) \]
Kubvisa Vector muZviyero Zvitatu
Pfungwa yekubvisa vhektari muzvikamu zvitatu yakafanana neiri muzvikamu zviviri. Kana \( \mathbf{a} = (a_1, a_2, a_3) \) uye \( \mathbf{b} = (b_1, b_2, b_3) \), saka:
\[ \mathbf{a} – \mathbf{b} = (a_1, a_2, a_3) – (b_1, b_2, b_3) = (a_1 – b_1, a_2 – b_2, a_3 – b_3) \]
Semuenzaniso, kana \( \mathbf{a} = (5, 7, 2) \) uye \( \mathbf{b} = (2, 3, 4) \), saka kubvisa ndekwekuti:
\[ \mathbf{a} – \mathbf{b} = (5 – 2, 7 – 3, 2 – 4) = (3, 4, -2) \]
Mutemo wekubvisa mavector
Mitemo yakati wandei inoshanda pakubvisa vhektari, yakafanana neiya yekuwedzera vhektari. Heino mitemo mikuru:
1. Kuchinja-chinja: Kubvisa kwevector hakusi kuchinja-chinja, zvichireva kuti:
\[ \mathbf{a} – \mathbf{b} \neq \mathbf{b} – \mathbf{a} \]
Semuenzaniso, kana \( \mathbf{a} = (4,3) \) uye \( \mathbf{b} = (1,2) \):
\[ \mathbf{a} – \mathbf{b} = (4-1, 3-2) = (3,1) \]
Asi:
\[ \mathbf{b} – \mathbf{a} = (1-4, 2-3) = (-3,-1) \]
2. Kubatanidza: Kubvisa vhekita pamwe chete nekuwedzera kunobatanidza, zvinoti:
\[ \mathbf{a} – (\mathbf{b} – \mathbf{c}) = (\mathbf{a} – \mathbf{b}) + \mathbf{c} \]
Mashandisirwo Ekubvisa Vector
Kubvisa mavector kunoshandiswa zvakanyanya muzvikamu zvakasiyana-siyana zvesainzi neinjiniya. Heano mimwe mienzaniso:
1. Fizikisi
Mufizikisi, kubvisa vhekitari kunoshandiswa kuona simba rinobuda, nguva, kutama, kumhanya kwehukama, nezvimwewo. Semuenzaniso, kana masimba maviri achishanda pachinhu, simba remambure rinogona kuverengerwa uchishandisa kubvisa vhekitari. Ngatitii masimba maviri \( \mathbf{F_1} \) uye \( \mathbf{F_2} \) achishanda pachinhu munzira dzakasiyana; simba remambure \( \mathbf{F} \) rinoverengerwa se:
\[ \mathbf{F} = \mathbf{F_1} – \mathbf{F_2} \]
2. Uinjiniya neTekinoroji
Muinjiniya yezvivakwa, kubvisa mavector kunogona kushandiswa kuongorora masimba anoshanda pazvivakwa, zvakaita semabhiriji kana zvivakwa. Semuenzaniso, mainjiniya vanogona kushandisa kubvisa mavector kuti vaone simba rinoshanda panzvimbo yakati muchivako nekuda kwemutoro wakaiswa.
3. Kufamba-famba uye Ndege
Mukufamba mumhepo nepagungwa, kubvisa mavector kwakakosha pakufamba munzira kubva pane imwe nzvimbo kuenda kune imwe, kunyanya kana paine kusagadzikana kwemhepo kana mafungu egungwa. Semuenzaniso, kana ndege iri kubhururuka nekumhanya kwakanangana nemhepo, kubvisa mavector kunoshandiswa kuona kumhanya kwechokwadi kwendege uye kuenda kwairi.
4. Marobhoti neMasisitimu Ekudzora
Mumarobhoti, kubvisa mavector kunoshandiswa kuronga nzira uye kudzivirira zvipingamupinyi. Marobhoti anofanira kuverenga nzvimbo yawo nemazvo zvichienderana nenzvimbo yawo.
Mienzaniso yekushandiswa kwekubvisa mavector
Ngatitii ngarava iri kufamba nekumhanya \( \mathbf{v_ship} \) uye yakanangana nemhepo yemvura ichifamba nekumhanya \( \mathbf{v_current} \). Kuti tizive kumhanya kwese kwengarava tichienzanisa nepasi, tinogona kushandisa kubvisa mafambiro emhepo:
\[ \mathbf{v_total} = \mathbf{v_ships} – \mathbf{v_current} \]
Ngatitii \( \mathbf{v_kapal} = (10, 15) \) km/h uye \( \mathbf{v_arus} = (2, 3) \) km/h, zvino:
\[ \mathbf{v_total} = (10 – 2, 15 – 3) = (8, 12) \] km/h.
Mhedziso
Kubvisa mavector ibasa guru rine mashandisirwo akakosha muminda yakasiyana-siyana. Kunzwisisa zvakanaka misimboti yayo mikuru nemashandisirwo ayo kunotibvumira kugadzirisa matambudziko akaomarara mufizikisi, mainjiniya, nedzimwe nzvimbo. Nekunzwisisa pfungwa huru, mitemo, uye mashandisirwo ekubvisa mavector, tinogona kuita ongororo nekuverenga zviri nyore zvinodiwa mumamiriro akasiyana-siyana ehunyanzvi nesainzi.
