Mavekitari Asina Kunaka kana Mavekitari Akasiyana: Pfungwa uye Mashandisirwo Muhupenyu
Vector chinhu chemasvomhu chine hukuru uye gwara. Mavector anoshandiswa muzvikamu zvakasiyana-siyana zvesainzi, zvakaita sefizikisi, masvomhu, uye engineering, kumiririra huwandu hunoda zvinopfuura kukosha kwenhamba chete. Imwe pfungwa yakakosha mukudzidza mavectors ivector isina kunaka, kana vector yakapesana. Chinyorwa chino chichakurukura tsananguro yevector isina kunaka, maitiro ekuiverenga, uye mashandisirwo ayo muzvikamu zvakasiyana-siyana zvehupenyu hwezuva nezuva.
Kunzwisisa Mafungiro Asina Kunaka
Vector isina kunaka, inozivikanwawo sevector yakapesana, ivector ine hukuru hwakafanana asi iine divi rakapesana nevector yekutanga. Kana vector yekutanga ichimiririrwa naA, saka vector yayo isina kunaka inowanzomiririrwa nechiratidzo \(-\mathbf{A}\). Nemamwe mashoko, zvinhu zvevector iyi zvine chiratidzo chakapesana nezvinhu zvevector yekutanga.
Pamasvomhu, kana \(\mathbf{A} = (a_1, a_2, \ldots, a_n)\), saka vhekitari isina kunaka ndeye \(-\mathbf{A} = (-a_1, -a_2, \ldots, -a_n)\). Izvi zvinoreva kuti chikamu chimwe nechimwe chevekitari yekutanga muCartesian coordinates chinoshandurwa kuita chiratidzo chakapesana muvekitari isina kunaka.
Maitiro Ekuverenga Mavector Asina Kunaka
Kuziva vhekitari isina kunaka kuri nyore kwazvo. Semuenzaniso, munzvimbo ine mativi maviri (2D), kana tine vhekitari \(\mathbf{A} = (3, 4)\), zvino:
\[
-\mathbf{A} = (-3, -4)
\]
Munzvimbo ine mativi matatu (3D), kana \(\mathbf{A} = (2, -1, 5)\), zvino:
\[
-\mathbf{A} = (-2, 1, -5)
\]
Kuongororwa kwemavector asina kunaka uku hakungogumiri pamavector ane mativi maviri kana matatu chete, asi kunogona kushandiswa kumavector ane mativi akakwirira.
Kushandiswa kweNegative Vectors muhupenyu hwezuva nezuva
Ma "negative vectors" ane mashandisirwo akasiyana-siyana muhupenyu hwezuva nezuva uye muzvikamu zvakasiyana-siyana. Heano mimwe mienzaniso:
1. Fizikisi neUinjiniya
Mufizikisi neinjiniya, pfungwa yemavector asina kunaka inokosha pakuongorora masimba nekufamba. Semuenzaniso, mu statics ne dynamics, pakuverenga masimba anoshanda pachinhu, tinowanzo fanirwa kufunga nezvemasimba ari kumativi akasiyana kuti tione poindi yekuenzana.
Mumwe muenzaniso ndewekufamba nendege. Kana ndege ikasangana nekuvhiringika, kuchinja kwenzira, kana kuchinja kwenzira yemhepo, mutyairi wendege anofanira kufunga nezvemhepo inopesana nayo kuti agadzirise nzira yekubhururuka.
2. Zvehupfumi neMari
Muhupfumi nezvemari, shanduko mumitengo kana maindices zvinomiririrwa nemavector. Semuenzaniso, kana mutengo wemasheya wanhasi ukadzikira zvichienzaniswa nemutengo wezuva rapfuura, shanduko yemutengo inogona kutorwa se negative vector.
Kuongorora kudzoreredzwa kwemamiriro ezvinhu, uko kunowanzo shandiswa muhupfumi kufanotaura mafambiro ezvinhu, kunogonawo kumirirwa nemavector, uye dzimwe nguva, tinofanira kufunga nezvezvinhu kana ma coefficients ari munzira yakasiyana (negative vectors) mumamodeli edu ekufanotaura.
3. Mifananidzo yeKombuta neMifananidzo
Mumifananidzo yemakombiyuta, mavector anoshandiswa kutsanangura nzvimbo, kurongeka, uye kufamba kwezvinhu. Mavector asina kunaka anoshandiswa kuita shanduko dzakadai sekutarisa nekudzosera shure gwara rekufamba kwehupenyu.
Semuenzaniso, pakuenzanisa chinhu che3D, tinogona kuwanza macoordinates echinhu nevector isina kunaka kuti tibudise kuratidzwa kwechinhu ichocho pane imwe axis.
4. Zvemaumbirwo enzvimbo
Mukuongorora geology, pfungwa yema "negative vectors" inoshandiswa kutsanangura kufamba kwema "tectonic plates", kusanganisira mafambiro adzo uye simba rekurova kwadzo. Ma "vectors" aya anobatsira vanoongorora geology kunzwisisa mashandiro ePasi uye kufanotaura zviitiko zvechisikigo zvakaita sekudengenyeka kwenyika.
Mienzaniso Yechokwadi Yenyaya
Kuti tijekese kushandiswa kwema negative vectors, tinogona kutarisa muenzaniso chaiwo unotevera mumunda wemakanika:
Fungidzira masimba maviri achishanda pane chimwe chinhu, chatichadaidza kuti \(\mathbf{F_1}\) uye \(\mathbf{F_2}\). Kana masimba aya achishanda nenzira imwe chete, simba rose ndiro huwandu hwemasimba maviri:
\[
\mathbf{F_{total}} = \mathbf{F_1} + \mathbf{F_2}
\]
Zvisinei, kana simba \(\mathbf{F_2}\) riri munzira yakasiyana ne \(\mathbf{F_1}\), saka:
\[
\mathbf{F_{total}} = \mathbf{F_1} + (-\mathbf{F_2})
\]
Semuenzaniso, ngatitii \(\mathbf{F_1} = (10, 15)\) Newton na \(\mathbf{F_2} = (5, 7)\) Newton vari munzira dzakasiyana, saka:
\[
-\mathbf{F_2} = (-5, -7)
\]
Saka simba rose rinoshanda pachinhu chacho nderinoti:
\[
\mathbf{F_{total}} = (10, 15) + (-5, -7) = (5, 8) \text{Newton}
\]
Kubva pakuverenga uku, zviri pachena kuti nekuwedzera mavector asina kunaka emasimba \(\mathbf{F_2}\), tinowana simba rose tichifunga nezvenzira dzakasiyana, zvichienderana nepfungwa yevector isina kunaka.
Mhedziso
Mavector asina kunaka, kana kuti mavector anopikisa, ipfungwa huru mukudzidza mavector uye ane mashandisirwo akapararira muzvikamu zvakasiyana-siyana zvesainzi nehupenyu hwezuva nezuva. Nekunzwisisa matsananguriro nekushandisa mavector asina kunaka, tinogona kurerutsa nekugadzirisa matambudziko akawanda akaomarara anoda kuongororwa kwegwara nehukuru.
Kuziva maverengero nekushandisa ma negative vectors kunotibvumira kuwana ruzivo rwakakura muzvidzidzo zvakaita sefizikisi, mainjiniya, economics, computer graphics, uye geology. Ma negative vectors haasi chishandiso chemasvomhu chete, asiwo chinhu chikuru chekugadzirisa matambudziko chaiwo anosanganisira kuongorora kwakazara kwegwara nehukuru.
