Imibuzo Eyisibonelo Exoxa Ngama-Vector Angalungile Noma Ama-Vector Aphambene
Ezibalweni, ikakhulukazi ku-physics noma ku-analytical geometry, umqondo wama-vector udlala indima ebalulekile. Ama-vector ngokuvamile asetshenziselwa ukumela amanani anesiqondiso kanye nobukhulu, njengejubane, amandla, kanye nokususwa. Lapho sixoxa ngama-vector, sivame ukuhlangana namagama athi "i-vector engemihle" noma "i-vector ephambene." Lesi sihloko sizochaza lo mqondo ngokujulile futhi sinikeze izibonelo nezixazululo zokwenza kube lula ukuqonda.
Incazelo yeVektha Engalungile
Ivektha engemihle, noma ivektha ephambene, iyivektha enesiqondiso esiphambene kodwa ubukhulu obufanayo nobevektha yokuqala. Uma sinevektha \(\mathbf{a}\), khona-ke ivektha engemihle ye-\(\mathbf{a}\), evame ukubizwa ngokuthi \(-\mathbf{a}\), inesiqondiso esiphambene futhi ubukhulu obufanayo ne-\(\mathbf{a}\). Uma i-\(\mathbf{a}\) imelelwe ngesimo sengxenye njenge-\((a_x, a_y)\), khona-ke ivektha engemihle ingu-\((-a_x, -a_y)\).
I-Vector Notation kanye Nokumelwa
Ake sithi i-vector \(\mathbf{a}\) imelelwe ngesimo sengxenye njenge:
\[ \mathbf{a} = a_x \mathbf{i} + a_y \mathbf{j} \]
lapho i-\(\mathbf{i}\) kanye ne-\(\mathbf{j}\) ziyi-unit vectors eziqondisweni ze-x- kanye ne-y, ngokulandelana. Ngemuva kwalokho, i-negative vector \(\mathbf{a}\) noma \(-\mathbf{a}\) ingamelwa kanje:
\[ -\mathbf{a} = -a_x \mathbf{i} – a_y \mathbf{j} \]
Izakhiwo Zezimvemvane Ezingalungile
Ezinye zezimpawu ezibalulekile zama-negative vectors zifaka:
1. Ukwengeza ngeVektha Yokuqala: Ukwengeza ivektha ngevektha yayo engemihle kuzokhiqiza ivektha engu-zero.
\[ \mathbf{a} + (-\mathbf{a}) = \mathbf{0} \]
2. Imisebenzi ye-Scalar: Ukuphindaphinda i-vector ngo--1 kuzokhiqiza i-vector yayo engemihle.
\[ -1 \cdot \mathbf{a} = -\mathbf{a} \]
Imibuzo Eyisibonelo Nengxoxo
Ukuze siqonde kangcono umqondo wamavektha angemihle noma amavektha aphikisanayo, ake sisebenzele ezinkingeni ezilandelayo zezibonelo:
Isibonelo 1:
Ake sithi kukhona i-vector \(\mathbf{a} = 3 \mathbf{i} – 4 \mathbf{j}\). Thola i-vector engemihle ye-vector \(\mathbf{a}\).
Ingxoxo:
Kuyaziwa:
\[ \mathbf{a} = 3 \mathbf{i} – 4 \mathbf{j} \]
Ivektha engemihle ye-\(\mathbf{a}\) ithi:
\[ -\mathbf{a} = -1 \cdot (3 \mathbf{i} – 4 \mathbf{j}) \]
\[ -\mathbf{a} = -3 \mathbf{i} + 4 \mathbf{j} \]
Ngakho-ke, ivektha engemihle ye- \(\mathbf{a}\) ithi:
\[ -\mathbf{a} = -3 \mathbf{i} + 4 \mathbf{j} \]
Isibonelo 2:
Kunamavekhtha amabili \(\mathbf{b} = 6 \mathbf{i} + 2 \mathbf{j}\) kanye \(\mathbf{c} = -1 \mathbf{i} + 7 \mathbf{j}\). Thola umkhiqizo we-\(\mathbf{b} + (-\mathbf{c})\).
Ingxoxo:
Kuyaziwa:
\[ \mathbf{b} = 6 \mathbf{i} + 2 \mathbf{j} \]
\[ \mathbf{c} = -1 \mathbf{i} + 7 \mathbf{j} \]
Ivektha engemihle ye-\(\mathbf{c}\) ithi:
\[ -\mathbf{c} = -1 \cdot (-1 \mathbf{i} + 7 \mathbf{j}) \]
\[ -\mathbf{c} = 1 \mathbf{i} – 7 \mathbf{j} \]
Manje sithola \(\mathbf{b} + (-\mathbf{c})\):
\[ \mathbf{b} + (-\mathbf{c}) = (6 \mathbf{i} + 2 \mathbf{j}) + (1 \mathbf{i} – 7 \mathbf{j}) \]
\[ \mathbf{b} + (-\mathbf{c}) = (6 + 1) \mathbf{i} + (2 – 7) \mathbf{j} \]
\[ \mathbf{b} + (-\mathbf{c}) = 7 \mathbf{i} – 5 \mathbf{j} \]
Ngakho-ke, umphumela we-\(\mathbf{b} + (-\mathbf{c})\) uthi:
\[ 7 \mathbf{i} – 5 \mathbf{j} \]
Isibonelo 3:
Kukhona i-vector \(\mathbf{d} = a \mathbf{i} + b \mathbf{j}\), lapho u-a no-b kuyizinombolo zangempela. Uma \(\mathbf{d} + \mathbf{e} = \mathbf{0}\), nquma i-vector \(\mathbf{e}\).
Ingxoxo:
Kuyaziwa:
\[ \mathbf{d} = a \mathbf{i} + b \mathbf{j} \]
\[ \mathbf{d} + \mathbf{e} = \mathbf{0} \]
Ukuze sithole \(\mathbf{e}\), singabhala:
\[ \mathbf{e} = -\mathbf{d} \]
Ngakho-ke, ivektha \(\mathbf{e}\) iyivektha engemihle ye-\(\mathbf{d}\):
\[ \mathbf{e} = -\mathbf{d} = -a \mathbf{i} – b \mathbf{j} \]
Isibonelo 4:
Kunikezwe i-vector \(\mathbf{f} = 5 \mathbf{i} + k \mathbf{j}\). Kuyaziwa ukuthi i-vector enegethivu ye-\(\mathbf{f}\) ithi \(-5 \mathbf{i} – 8 \mathbf{j}\). Thola inani le-k.
Ingxoxo:
Kuyaziwa:
\[ \mathbf{f} = 5 \mathbf{i} + k \mathbf{j} \]
\[ -\mathbf{f} = -5 \mathbf{i} – 8 \mathbf{j} \]
Kusukela kulobu budlelwano, singakha izilinganiso zezingxenye ze-\(\mathbf{f}\) kanye ne-\(-\mathbf{f}\). Ngokwengxenye, i-vector \(\mathbf{f}\) kanye ne-vector yayo engemihle kumele ibe nobudlelwano obufanayo besimo nezimpawu eziphambene. Ngakho-ke:
Ngezingxenye \( \mathbf{i} \):
\[ -5 = -5 \]
Lokhu kuyiqiniso ngokuzenzakalelayo.
Kwengxenye \( \mathbf{j} \):
\[ -k = -8 \]
\[k = 8 \]
Ngakho-ke, inani lika-\( k \) lingu-8.
Isiphetho
Ukuqonda umqondo wevektha engemihle, noma ivektha ephambene, kubalulekile ekutadisheni amavektha. Ivektha ephambene iyivektha ephambene nevektha yokuqala kodwa inobukhulu obufanayo. Emisebenzini yamavektha, ukuqaphela nokusebenzisa amavektha angemihle kungaba usizo kakhulu ekwenzeni lula izinkinga eziningi, njengokwengeza noma ukususa amavektha. Ngokuzijwayeza nokuqonda izakhiwo eziyisisekelo zamavektha, ukuqonda lo mqondo kuzoba lula kakhulu.
Sithemba ukuthi imibuzo eyisibonelo kanye nengxoxo evezwe kulesi sihloko izokusiza ukuthi uthole ukuqonda okujulile ngama-vector angemihle, noma ama-vector aphikisanayo. Qhubeka uzijwayeza futhi uhlole imibuzo eminingi ukuze ube nekhono kakhudlwana kulokhu okusetshenziswayo!
