Li-vector tse mpe kapa li-vector tse fapaneng: Khopolo le ts'ebeliso bophelong
Vekthara ke ntho ea lipalo e nang le boholo le tataiso. Livekthara li sebelisoa mafapheng a fapaneng a saense, joalo ka fisiks, lipalo le boenjiniere, ho emela bongata bo hlokang ho feta boleng ba lipalo feela. Khopolo e 'ngoe ea bohlokoa thutong ea livekthara ke vekthara e mpe, kapa vekthara e fapaneng. Sehlooho sena se tla tšohla tlhaloso ea vekthara e mpe, mokhoa oa ho e bala, le ts'ebeliso ea eona likarolong tse fapaneng tsa bophelo ba letsatsi le letsatsi.
Ho Utloisisa Li-vector tse Fosahetseng
Vekthara e mpe, e tsejoang hape e le vekthara e fapaneng, ke vekthara e nang le boholo bo tšoanang empa e le lehlakoreng le fapaneng le vekthara ea pele. Haeba vekthara ea pele e emetsoe ke A, joale vekthara ea eona e mpe hangata e emetsoe ke letšoao \(-\mathbf{A}\). Ka mantsoe a mang, likarolo tsa vekthara ena li na le letšoao le fapaneng le likarolo tsa vekthara ea pele.
Ho ya ka dipalo, haeba \(\mathbf{A} = (a_1, a_2, \ldots, a_n)\), jwale vektara e mpe ke \(-\mathbf{A} = (-a_1, -a_2, \ldots, -a_n)\). Sena se bolela hore karolo e nngwe le e nngwe ya vektara ya pele ho di-coordinate tsa Cartesian e fetolwa ho ba letshwao le fapaneng ho vektara e mpe.
Mokhoa oa ho Bala Li-vector tse mpe
Ho fumana vekthara e mpe ho bonolo haholo. Mohlala, sebakeng sa mahlakore a mabedi (2D), haeba re na le vekthara \(\mathbf{A} = (3, 4)\), ebe:
\[
-\mathbf{A} = (-3, -4)
\]
Sebakeng sa mahlakore a mararo (3D), haeba \(\mathbf{A} = (2, -1, 5)\), joale:
\[
-\mathbf{A} = (-2, 1, -5)
\]
Tlhahlobo ena ea li-vector tse mpe ha e felle feela ho li-vector tse peli kapa tse tharo feela, empa e ka sebelisoa ho li-vector tse nang le litekanyo tse phahameng.
Tšebeliso ea Li-vector tse mpe bophelong ba letsatsi le letsatsi
Li-vector tse mpe li na le mefuta e fapaneng ea lits'ebetso tsa lefats'e la nnete bophelong ba letsatsi le letsatsi le mafapheng a fapaneng. Mehlala e meng ke ena:
1. Fisiks le Boenjiniere
Fisiks le boenjiniere, khopolo ea li-vector tse mpe e bohlokoa haholo tlhahlobong ea matla le motsamao. Mohlala, ho statics le dynamics, ha re bala matla a sebetsang nthong, hangata re hloka ho nahana ka matla ka mahlakoreng a fapaneng ho fumana ntlha ea tekano.
Mohlala o mong ke oa lifofane le ho tsamaea ka sekepe. Ha sefofane se kopana le moferefere, phetoho tseleng, kapa phetoho tseleng ea moea, mofofisi o tlameha ho nahana ka vector ea moea e khahlanong le sona ho lokisa tsela ea sefofane.
2. Moruo le Lichelete
Moruong le licheleteng, liphetoho lithekong kapa li-indices li emeloa ke li-vector. Mohlala, haeba theko ea setoko sa kajeno e theoha ha e bapisoa le theko ea letsatsi le fetileng, phetoho ea theko e ka nkoa e le vector e mpe.
Tlhahlobo ea ho khutlela morao, e atisang ho sebelisoa moruong ho bolela esale pele mekhoa, e ka boela ea emeloa ke li-vector, 'me ka linako tse ling, re tlameha ho nahana ka lintlha kapa li-coefficient tse ka lehlakoreng le fapaneng (li-vector tse mpe) mehlala ea rona ea ho bolela esale pele.
3. Litšoantšo tsa Khomphutha le Lipopae
Litšoantšong tsa khomphutha, li-vector li sebelisoa ho hlalosa boemo, tataiso le motsamao oa lintho. Li-vector tse mpe li sebelisoa ho etsa liphetoho tse kang ho bonahatsa le ho khutlisetsa morao tataiso ea motsamao o phelang.
Mohlala, ha re etsisa ntho ea 3D, re ka atisa likhokahano tsa ntho ka vekthara e mpe ho hlahisa ponts'o ea ntho eo mothating o itseng.
4. Thuto ea Mafika
Thutong ea jeoloji, khopolo ea li-vector tse mpe e sebelisoa ho hlalosa motsamao oa lipoleiti tsa tectonic, ho kenyeletsoa le tataiso ea ho falla ha tsona le matla a tšusumetso ea tsona. Li-vector tsena li thusa litsebi tsa jeoloji ho utloisisa matla a Lefatše le ho bolela esale pele liketsahalo tsa tlhaho tse kang litšisinyeho tsa lefatše.
Mehlala ea Nyeoe ea 'Nete
Ho hlakisa ts'ebeliso ea li-vector tse mpe, re ka sheba mohlala o latelang oa 'nete lefapheng la mechini:
Ak'u nahane ka matla a mabeli a sebetsang nthong, eo re tla e bitsa \(\mathbf{F_1}\) le \(\mathbf{F_2}\). Haeba matla ana a sebetsa ka lehlakoreng le le leng, matla a felletseng ke kakaretso ea matla a mabeli:
\[
\mathbf{F_{kakaretso}} = \mathbf{F_1} + \mathbf{F_2}
\]
Leha ho le jwalo, haeba matla \(\mathbf{F_2}\) a le ka lehlakoreng le fapaneng le \(\mathbf{F_1}\), jwale:
\[
\mathbf{F_{kakaretso}} = \mathbf{F_1} + (-\mathbf{F_2})
\]
Mohlala, a re re \(\mathbf{F_1} = (10, 15)\) Newton le \(\mathbf{F_2} = (5, 7)\) Newton li ka mahlakoreng a fapaneng, ebe:
\[
-\mathbf{F_2} = (-5, -7)
\]
Kahoo matla ohle a sebetsang nthong ke:
\[
\mathbf{F_{total}} = (10, 15) + (-5, -7) = (5, 8) \text{ Newton}
\]
Ho tsoa palong ena, ho hlakile hore ka ho eketsa li-vector tse mpe tsa matla \(\mathbf{F_2}\), re fumana matla a felletseng re nahana ka litsela tse fapaneng, ho latela mohopolo oa vector e mpe.
Qetello
Li-vector tse mpe, kapa li-vector tse hanyetsanang, ke mohopolo oa motheo thutong ea li-vector 'me li na le lits'ebetso tse pharaletseng mafapheng a fapaneng a mahlale le bophelo ba letsatsi le letsatsi. Ka ho utloisisa mokhoa oa ho hlalosa le ho sebelisa li-vector tse mpe, re ka nolofatsa le ho rarolla mathata a mangata a rarahaneng a hlokang tlhahlobo ea tataiso le boholo.
Ho tseba ho bala le ho sebelisa li-vector tse mpe ho re lumella ho fumana temohisiso e kholoanyane lithutong tse kang fisiks, boenjiniere, moruo, litšoantšo tsa khomphutha le jeoloji. Li-vector tse mpe ha se sesebelisoa sa lipalo feela, empa hape ke senotlolo sa ho rarolla liphephetso tsa lefats'e la nnete tse kenyelletsang tlhahlobo e felletseng ea tataiso le boholo.
