Ukususa Amavektha: Izisekelo, Imithetho, kanye Nezicelo
Ukususa amavektha kuyisici esiyisisekelo sezibalo, i-physics, kanye nobunjiniyela. Empilweni yansuku zonke, sivame ukubhekana nezimo lapho sidinga ukususa amavektha amabili noma ngaphezulu, isibonelo ekubaleni isiqondiso somoya noma ukunyakaza kwezinto. Lesi sihloko sizoxoxa ngokujula kokunciphisa amavektha, okuhlanganisa nencazelo yawo, izimiso eziyisisekelo, imithetho, kanye nokusetshenziswa emikhakheni eyahlukahlukene.
Incazelo yeVektha
Ivektha iyinani elinobukhulu (noma ubude) kanye nesiqondiso. Izibonelo zamavektha zifaka phakathi ijubane, ukusheshisa, amandla, kanye nensimu kagesi. Amavektha ngokuvamile amelelwa njengemicibisholo kumadayagramu, lapho ubude bomcibisholo bubonisa ubukhulu kanye nesiqondiso somcibisholo sibonisa isiqondiso senani.
Ngokwezibalo, amavekhtha anezilinganiso ezimbili avame ukubhalwa ngesimo \( \mathbf{a} = (a_1, a_2) \) noma ngesimo esijwayelekile \( \mathbf{a} = ai + bj \), lapho \( i \) kanye \( j \) kuyivekhtha yeyunithi eziqondisweni ze-x- kanye ne-y.
Ukususa Amavektha: Imiqondo Eyisisekelo
Ukususa amavektha empeleni kungumsebenzi wokwengeza amavektha angemihle. Uma sinevektha ezimbili \( \mathbf{a} \) kanye \( \mathbf{b} \), khona-ke ukususa \( \mathbf{a} – \mathbf{b} \) kufana no \( \mathbf{a} + (-\mathbf{b}) \). Ivektha engemihle yevektha \( \mathbf{b} \) iyivektha enobukhulu obufanayo kodwa ephambene.
Ngokwezibalo, uma \( \mathbf{a} = (a_1, a_2) \) kanye \( \mathbf{b} = (b_1, b_2) \), khona-ke:
\[ \mathbf{a} – \mathbf{b} = (a_1, a_2) – (b_1, b_2) = (a_1 – b_1, a_2 – b_2) \]
Isibonelo Sokususa Amavektha Ngobukhulu Obubili
Ake sithi sinezivektha ezimbili ngobukhulu obubili, \( \mathbf{a} = (4, 3) \) kanye \( \mathbf{b} = (1, 2) \). Ukususa kwalezi zivektha ezimbili yilokhu:
\[ \mathbf{a} – \mathbf{b} = (4 – 1, 3 – 2) = (3, 1) \]
Ukususa Amavektha Ngobukhulu Obuthathu
Umqondo wokukhipha i-vector ngezilinganiso ezintathu ufana nalowo ongezilinganiso ezimbili. Uma \( \mathbf{a} = (a_1, a_2, a_3) \) kanye \( \mathbf{b} = (b_1, b_2, b_3) \), khona-ke:
\[ \mathbf{a} – \mathbf{b} = (a_1, a_2, a_3) – (b_1, b_2, b_3) = (a_1 – b_1, a_2 – b_2, a_3 – b_3) \]
Isibonelo, uma \( \mathbf{a} = (5, 7, 2) \) kanye \( \mathbf{b} = (2, 3, 4) \), khona-ke ukususa kungu:
\[ \mathbf{a} – \mathbf{b} = (5 – 2, 7 – 3, 2 – 4) = (3, 4, -2) \]
Umthetho Wokususa Ama-Vector
Imithetho eminingana eyisisekelo iyasebenza ekususweni kwe-vector, efana naleyo yokwengeza i-vector. Nansi imithetho eyinhloko:
1. Ukushintshashintsha: Ukususa amavektha akusikho ukushintshashintsha, okusho ukuthi:
\[ \mathbf{a} – \mathbf{b} \neq \mathbf{b} – \mathbf{a} \]
Isibonelo, uma \( \mathbf{a} = (4,3) \) kanye \( \mathbf{b} = (1,2) \):
\[ \mathbf{a} – \mathbf{b} = (4-1, 3-2) = (3,1) \]
Kanti:
\[ \mathbf{b} – \mathbf{a} = (1-4, 2-3) = (-3,-1) \]
2. Ukuhlanganisa: Ukususa amavektha kuhlanganiswe nokuhlanganisa kuyinhlanganisela, okungukuthi:
\[ \mathbf{a} – (\mathbf{b} – \mathbf{c}) = (\mathbf{a} – \mathbf{b}) + \mathbf{c} \]
Izinhlelo Zokususa Amavektha
Ukususa amavektha kusetshenziswa kabanzi emikhakheni eyahlukene yesayensi nobunjiniyela. Nazi ezinye izibonelo:
1. Ifiziksi
Ku-physics, ukukhipha amavektha kusetshenziselwa ukunquma amandla aphumayo, umzuzu, ukufuduka, ijubane elihlobene, nokuningi. Isibonelo, uma amandla amabili esebenza entweni, amandla aphelele angabalwa kusetshenziswa ukukhipha amavektha. Ake sithi amandla amabili \( \mathbf{F_1} \) kanye \( \mathbf{F_2} \) asebenza entweni ngezindlela eziphambene; amandla aphelele \( \mathbf{F} \) abalwa kanje:
\[ \mathbf{F} = \mathbf{F_1} – \mathbf{F_2} \]
2. Ubunjiniyela kanye nobuchwepheshe
Kubunjiniyela bezokwakha, ukususwa kwevektha kungasetshenziswa ukuhlaziya amandla asebenza ezakhiweni, njengamabhuloho noma izakhiwo. Isibonelo, onjiniyela bangasebenzisa ukususwa kwevektha ukuthola amandla asebenza endaweni ethile esakhiweni ngenxa yomthwalo osetshenzisiwe.
3. Ukuzulazula kanye nezindiza
Ekuzulazuleni emoyeni nasolwandle, ukususwa kwe-vector kubalulekile ekuzulazuleni imizila ukusuka endaweni eyodwa kuya kwenye, ikakhulukazi uma kukhona ukuphazamiseka komoya noma imisinga yolwandle. Isibonelo, uma indiza indiza ngesivinini esithile ibhekene nomoya, ukususwa kwe-vector kusetshenziselwa ukuthola isivinini sangempela sendiza kanye nokuya kwayo.
4. Izinhlelo Zamarobhothi Nokulawula
Kumarobhothi, ukususwa kwevektha kusetshenziselwa ukuhlela indlela kanye nokugwema izithiyo. Amarobhothi kudingeka abale ngokunembile indawo yawo maqondana nendawo akuyo.
Izibonelo Zokusetshenziswa Kokususa Amavektha
Ake sithi umkhumbi uhamba ngesivinini \( \mathbf{v_ship} \) futhi uqondiswe kumsinga wamanzi ohamba ngesivinini \( \mathbf{v_current} \). Ukuze sithole isivinini esiphelele somkhumbi maqondana nomhlabathi, singasebenzisa ukususwa kwevektha:
\[ \mathbf{v_total} = \mathbf{v_ships} – \mathbf{v_current} \]
Ake sithi \( \mathbf{v_kapal} = (10, 15) \) km/h kanye \( \mathbf{v_arus} = (2, 3) \) km/h, bese:
\[ \mathbf{v_total} = (10 – 2, 15 – 3) = (8, 12) \] km/h.
Isiphetho
Ukususa amavektha kuwumsebenzi oyisisekelo onezinhlelo zokusebenza ezibalulekile emikhakheni eyahlukahlukene. Ukuqonda kahle izimiso zayo eziyisisekelo kanye nezinhlelo zokusebenza kusenza sikwazi ukuxazulula izinkinga eziyinkimbinkimbi ku-physics, ubunjiniyela, kanye neminye imikhakha. Ngokuqonda imiqondo eyisisekelo, imithetho, kanye nezinhlelo zokusebenza zokususa amavektha, singenza kalula ukuhlaziya kanye nokubala okudingekayo ezimweni ezahlukahlukene zobungcweti nezesayensi.
