Ukuxoxa ngamavekhtha kuzibalo akuhlukaniseki engxoxweni yohlelo lwe-Cartesian coordinate. Uhlelo lwe-Cartesian coordinate luyisistimu esetshenziswa kakhulu ekwenzeni amamodeli nokuhlaziya izimo ezahlukahlukene esikhaleni esinezinhlangothi ezimbili nezintathu. Kulesi sihloko, sizohlola umqondo wamavekhtha alinganayo kumongo wohlelo lwe-Cartesian coordinate.
Isingeniso kumaVectors ohlelweni lweCartesian Coordinate
Kuhlelo lwe-Cartesian coordinate, iphuzu ngalinye esikhaleni esinezinhlangothi ezimbili lingamelwa njengepheya elihlelekile (x, y), lapho u-x eyi-coordinate evundlile kanye no-y eyi-coordinate eqondile. Esikhaleni esinezinhlangothi ezintathu, sine-triplet (x, y, z). I-vector kulo mongo iyinhlangano yezibalo enokukhulu (noma ubude) kanye nesiqondiso.
Ivektha esikhaleni esinezinhlangothi ezimbili ivame ukumelwa njengo-\(\vec{v}\) = (v_x, v_y), lapho \(v_x\) kanye no-\(v_y\) kuyizingxenye zevektha eceleni kwe-x-axis kanye ne-y-axis, ngokulandelana. Esikhaleni esinezinhlangothi ezintathu, ivektha imelelwa njengo-\(\vec{v}\) = (v_x, v_y, v_z).
Umqondo Wokulingana Kwevektha
Kuthiwa amavektha amabili ayalingana uma enobukhulu obufanayo kanye nesiqondiso esifanayo, kungakhathaliseki ukuthi aqala kuphi. Ngokwezibalo, amavektha amabili \(\vec{u}\) = (u_x, u_y) kanye \(\vec{v}\) = (v_x, v_y) kuthiwa ayalingana uma:
1. \(u_x = v_x\)
2. \(u_y = v_y\)
Empeleni, ama-vector awaboshelwe endaweni ethile yokuqala. Ama-vector amabili angabekwa noma kuphi esikhaleni, kodwa uma enesiqondiso nobukhulu obufanayo, asabhekwa njengalingana, noma alingana. Lesi yisici esibalulekile esenza ama-vector abe ithuluzi eliguquguqukayo kakhulu kwizibalo kanye ne-physics.
Isifaniso seJiyomethri
Ake sithi sinezivektha ezimbili \(\vec{u}\) = (3, 4) kanye \(\vec{v}\) = (3, 4). Lawa mavektha amabili, uma ebonakala ohlelweni lwe-Cartesian coordinate, azomelela imicibisholo eseceleni elifanayo futhi enobude obufanayo, noma ngabe angaqala ngamaphuzu ahlukene. Ngakho-ke, uma sidweba \(\vec{u}\) kusukela ekuqaleni (0, 0) kuya ephuzwini (3, 4) kanye \(\vec{v}\) kusukela ekuqaleni okuhlukile, ake sithi (1, 1), kuya ephuzwini (4, 5), lawa mavektha amabili asalingana ngoba anesiqondiso nobukhulu obufanayo.
Ukumelwa Kwevektha Elilinganayo Kuzibalo
Ngokwezibalo, ama-vector alinganayo alandela lesi simiso esilandelayo:
– Uma i-\(\vec{v}\) = (v_x, v_y) iyi-vector, khona-ke noma iyiphi i-vector elingana ne-\(\vec{v}\) ingatholakala ngokungeza i-vector efanayo yokuhumusha ezindaweni zayo zokuqala nezokugcina.
– Ngokwesiko, uma \(\vec{v_1}\) = (v_{1x}, v_{1y}) kanye \(\vec{v_2}\) = (v_{2x}, v_{2y}) kuyi-vector ezimbili ezilinganayo, khona-ke kukhona i-vector engaguquki \(\vec{k}\) = (k_x, k_y) yokuthi:
\[
\vec{v_1} = \vec{v_2} + \vec{k} – \vec{k}
\]
Le ngxenye ibamba isikhala esinobukhulu obungu-n futhi igcizelela iqiniso lokuthi ama-vector empeleni amayelana nomehluko ezikhundleni, hhayi ezikhundleni ngokwazo.
Ukusetshenziswa Kwama-Vector Alinganayo ku-Physics
Ku-physics, umqondo wamavektha alinganayo ubalulekile, ikakhulukazi ekuhlaziyweni kwamandla, ijubane, kanye nomfutho. Isibonelo, amandla asebenza endaweni ethile entweni angahunyushwa (njengamavektha alinganayo) uma ekhiqiza umphumela ofanayo maqondana nokusheshisa okuqondile noma ushintsho kumfutho.
Izibonelo Zokusetshenziswa:
1. Amandla Namavektha Alinganayo:
Kumakhenikhi akudala, uma amandla u-F emelelwa njengevektha futhi esetshenziswa endaweni ethile entweni, singahambisa indawo yokusetshenziswa kwamandla ngebanga elilinganayo. Lokhu kubalulekile ekubalweni kwezikhathi zamandla noma ama-torque, lapho izingxenye zamandla ezilinganayo zisetshenziswa khona ukuxazulula izinkinga zemishini.
2. Isivinini:
Ijubane njengevektha liveza isiqondiso kanye nesivinini sokunyakaza kwento. Isibonelo, ijubane lemoto eliya empumalanga ku-60 km/h lingamelwa njengevektha (60, 0) uma i-x-axis ikhomba empumalanga. Zonke ivektha ezilinganayo zichaza izimo zokunyakaza ezifanayo, noma ngabe izindawo zazo zokuqala zihlukile, isib. (1, 1) kuya ku-(61, 1).
Ama-Coordinates afanayo kanye nama-Vectors alinganayo
Esikhaleni esinezinhlangothi ezintathu, sivame ukusebenzisa ama-homogeneous coordinates ukwandisa ukuhlaziywa kwethu. Lolu hlelo lwethula i-matrix operator projection matrix, ekhulisa ukuqonda kwethu ama-vector alinganayo. Ama-homogeneous coordinates avame ukusetshenziswa kuma-computer graphics ukuze kube lula ukuguqulwa kwe-geometric njengokujikeleza, ukuhumusha, kanye nokulinganisa. Kulesi simo, ama-homogeneous vectors asivumela ukuthi senze ukuphathwa okufanayo nokuhle kuma-Cartesian coordinates.
Isiphetho
Amavekhtha alinganayo ohlelweni lwe-Cartesian coordinate angumqondo oyisisekelo owakha isisekelo sezicelo eziningi zezibalo kanye ne-physics. Ukuqonda lo mqondo kuhilela ukwazi ukuthi amavekhtha amabili ayalingana uma enesiqondiso nobukhulu obufanayo, noma ngabe amaphuzu okuqala angase ahluke. Ukumelwa kwezibalo kwamavekhtha alinganayo kubonisa ukuthi le mpahla ivumela ukuhambisa amaphuzu okuqala nawokugcina amavekhtha ngaphandle kokushintsha izakhiwo zawo eziyisisekelo.
Ukusetshenziswa kwalomqondo emikhakheni eyahlukene, njengefiziksi, kugcizelela ukubaluleka kokuqonda inkolelo-mbono yevektha ukuze kuhlaziywe kabanzi. Ezweni langempela, umqondo wamavektha alinganayo uvumela ukubalwa okulula kwamandla, amajubane, kanye nezinye izici eziningi ze-mechanics kanye ne-kinematics.
Njengoba sinekhono lokumela nokulawula ama-vector ohlelweni lwe-Cartesian coordinate, singayila futhi sihlaziye izinhlobo eziningi zezimo eziyinkimbinkimbi nezinhlelo ngezinga eliphezulu lokunemba nokunemba. Lokhu kwenza umqondo wama-vector alinganayo ube yisihloko esibalulekile nesithakazelisayo esifundweni sezibalo kanye ne-physics.
