Hoʻohui ʻāpana o nā Vectors
I ka makemakika a me ke kino, he manaʻo nui nā vectors. Hoʻohana ʻia lākou e wehewehe i nā nui i loaʻa ke kuhikuhi a me ka nui. He mea koʻikoʻi ka ʻike o ka hoʻohui vector i nā ʻano noi ʻepekema a me nā ʻenehana like ʻole. ʻO kekahi o nā ʻano hana maʻamau no ka hoʻohui ʻana i nā vectors ʻo ia ka hoʻohui ʻana i nā ʻāpana. E wehewehe kēia ʻatikala i nā kumumanaʻo kumu o ka hoʻohui vector, ke kumumanaʻo o nā ʻāpana vector, a me nā ʻanuʻu no ka hoʻohui ʻana i nā vectors i nā ʻāpana.
He aha ka Vector?
Ma mua o ke komo ʻana i ka hoʻohui vector, pono mākou e hoʻomaopopo i ke ʻano o ka vector. He mea makemakika ka vector me ʻelua mau ʻano nui: ka nui (a i ʻole ka lōʻihi) a me ke kuhikuhi. ʻO kahi laʻana maʻalahi o kahi vector i ke ola o kēlā me kēia lā, ʻo ia ka neʻe ʻana o kahi mea. No ka laʻana, inā hele kekahi i 5 kilomita ma ka ʻākau, hiki iā mākou ke hōʻike i kēlā huakaʻi me kahi vector me ka nui o 5 kilomita a me ke kuhikuhi o ka ʻākau.
Hoʻohālikelike pinepine ʻia nā vectors ma ke ʻano he mau pua, kahi e hōʻike ai ka lōʻihi o ka pua i ka nui a ʻo ke kuhikuhi o ka pua e hōʻike ana i ka vector. Hiki ke hōʻike ʻia nā vectors ma ke ʻano he mau ʻāpana e like me nā axis coordinate, e like me nā axis x, y, a me z i loko o kahi ʻōnaehana coordinate ʻekolu-dimensional.
Nā ʻĀpana Vector
Hiki ke hoʻokaʻawale ʻia kahi vector ma nā ana ʻelua a ʻekolu paha i nā ʻāpana e like me nā axis coordinate. No ka laʻana, hiki ke hoʻokaʻawale ʻia kahi vector ʻelua-dimensional me ka waiwai (3, 4) me kahi ʻāpana x = 3 a me kahi ʻāpana y = 4. Ma nā huaʻōlelo geometric, ʻo ia hoʻi, hiki ke nānā ʻia ka vector ma ke ʻano he huina o ʻelua vectors: hoʻokahi vector e like me ke axis-x me ka nui 3, a hoʻokahi vector e like me ke axis-y me ka nui 4.
No kahi vector ʻekolu-dimensional, loaʻa iā mākou ʻekolu mau ʻāpana: x, y, a me z. No ka laʻana, ʻo ka vector (3, 4, 5) he mau ʻāpana x = 3, y = 4, a me z = 5. I loko o kahi ʻōnaehana hoʻonohonoho Cartesian, hiki ke hōʻike ʻia kēia vector ma ke ʻano he pua e hoʻomaka ana mai ke kumu (0, 0, 0) a hoʻopau ma ke kiko (3, 4, 5).
Hoʻohui ʻāpana o nā Vectors
I kēia manawa, e kūkākūkā kākou pehea e hoʻohui ai i nā vectors me ka hoʻohana ʻana i ke ʻano componentwise. ʻO ka hoʻohui vector Componentwise e pili ana i ka hoʻohui ʻana i kēlā me kēia ʻāpana ma ke kaʻawale. He ʻano hana kūpono a maikaʻi loa kēia, ʻoiai ke hana nei me nā vectors i loko o kahi ʻōnaehana hoʻonohonoho Cartesian.
Nā ʻanuʻu no ka hoʻohui ʻāpana o nā Vectors
1. E hoʻokaʻawale i ka vector i loko o kona mau ʻāpana:
Ma ke ʻano he hana mua, pono mākou e hoʻokaʻawale i kēlā me kēia vector e hoʻohui ʻia i loko o kona mau ʻāpana e like me nā koʻi x, y, a me z (inā he).
2. Hoʻohui ʻia o nā ʻāpana like:
No kēlā me kēia axis (x, y, a me z), hoʻohui mākou i nā ʻāpana like. No ka laʻana, ʻo ka ʻāpana-x o ka huina ka huina o nā ʻāpana-x āpau o nā vectors e hoʻohui ʻia ana.
3. E hoʻohui hou i nā ʻāpana i hoʻohui ʻia:
Ma hope o ka hoʻohui ʻia ʻana o nā ʻāpana a pau, hoʻohui hou mākou i nā ʻāpana e loaʻa ai ka vector huina.
E nānā kākou i kahi laʻana paʻa e hoʻomālamalama hou aku i kēia manaʻo.
Laʻana o ka Hoʻohui Vector ma nā Ana ʻElua
Manaʻo mākou he ʻelua vectors i ʻelua mau ana:
– Vector A = (3, 4)
– Vector B = (1, 2)
KaʻAnuʻu Hana 1: E hoʻokaʻawale i kēlā me kēia vector i loko o kona mau ʻāpana:
– A_x = 3, A_y = 4
– B_x = 1, B_y = 2
KaʻAnuʻu Hana 2: Hoʻohui i nā ʻāpana like:
– Hopena o ka ʻāpana x: A_x + B_x = 3 + 1 = 4
– Hopena o ka ʻāpana y: A_y + B_y = 4 + 2 = 6
KaʻAnuʻu Hana 3: E hoʻohui hou i nā ʻāpana i hoʻohui ʻia:
– Vector hopena = (4, 6)
No laila, ʻo ka hopena o ka hoʻohui ʻana i nā vectors A a me B he vector (4, 6).
Laʻana o ka Hoʻohui Vector ma nā Ana ʻEkolu
Hiki iā kākou ke hoʻonui i kēia laʻana i ʻekolu ana. Manaʻo mākou he ʻelua vectors i ʻekolu ana:
– Vector C = (2, -1, 3)
– Vector D = (1, 4, -2)
KaʻAnuʻu Hana 1: E hoʻokaʻawale i kēlā me kēia vector i loko o kona mau ʻāpana:
– C_x = 2, C_y = -1, C_z = 3
– D_x = 1, D_y = 4, D_z = -2
KaʻAnuʻu Hana 2: Hoʻohui i nā ʻāpana like:
– Hopena o ka ʻāpana x: C_x + D_x = 2 + 1 = 3
– Hopena o ka ʻāpana y: C_y + D_y = -1 + 4 = 3
– Hopena o ka ʻāpana z: C_z + D_z = 3 – 2 = 1
KaʻAnuʻu Hana 3: E hoʻohui hou i nā ʻāpana i hoʻohui ʻia:
– Vector hopena = (3, 3, 1)
ʻO ka hopena o ka hoʻohui ʻana i nā vectors C a me D ʻo ia ka vector (3, 3, 1).
Ke Koʻikoʻi o ka Hoʻohui Vector i ke Ola o kēlā me kēia lā
ʻOiai ke ʻano o ka hoʻohui vector ma ke ʻano he kumuhana esoteric, he mau noi kūpono kona i ke ola o kēlā me kēia lā a me nā ʻano loea like ʻole. ʻO kekahi mau laʻana o nā noi:
1. ʻIke Kino: Nui nā manaʻo i ka ʻike kino, e like me ka ikaika, ka wikiwiki, a me ka wikiwiki, i hōʻike ʻia ma ke ʻano he vectors. Hoʻohana pinepine ʻia ka hoʻohui vector e helu i ka hopena o ka ikaika a i ʻole ka wikiwiki.
2. ʻEnekinia: I ka ʻenekinia, hoʻohana ʻia nā vectors no ka nānā ʻana i ke ʻano, ka dynamics wai, a me ka electromagnetism. ʻO ka hoʻohui ʻāpana o nā vectors e kōkua i nā ʻenekinia e hoʻolālā a kālailai i nā ʻōnaehana paʻakikī.
3. Nā Kiʻi Kamepiula: Hoʻohana ʻia nā vectors i nā kiʻi kamepiula e wehewehe i ke kūlana, ka wikiwiki, a me ka wikiwiki o nā mea. He mea nui ka hoʻohui vector ma ke ʻano he ʻāpana i ka hoʻomohala ʻana i ka animation a me ka simulation.
4. Hoʻokele: I ka hoʻokele ʻana, inā ma ka ʻāina, ke kai, a i ʻole ka lewa, hoʻohana ʻia ka hoʻohui vector e hoʻoholo ai i ke ala a me ke kūlana. ʻO ka ʻenehana GPS, no ka laʻana, hoʻohana i nā loina vector e helu i ke ala kūpono loa.
Ma ka hoʻomaopopo ʻana i nā manaʻo kumu a me nā hoʻohana pono o ka hoʻohui vector componentwise, hiki iā mākou ke mahalo i ke koʻikoʻi o nā vectors ma nā ʻano like ʻole o ke ola hou a me ka ʻenehana.
Ka hopena
ʻO ka hoʻohui vector componential kahi ʻano hana kūpono a kūpono hoʻi no ka hoʻohui ʻana i nā vectors i loko o kahi ʻōnaehana hoʻonohonoho Cartesian. Ma ka hoʻokaʻawale ʻana i kahi vector i loko o kona mau ʻāpana e like me nā axis coordinate, hiki iā mākou ke hoʻohui maʻalahi i kēlā mau ʻāpana ma mua o ka hoʻohui ʻana iā lākou e loaʻa ai ka vector hopena. He nui nā noi kūpono o kēia ʻano hana i ka physics, ka ʻenekinia, nā kiʻi kamepiula, ka hoʻokele, a me nā mea hou aku. ʻO ka hoʻomaopopo ʻana i ka hoʻohui vector componential ʻaʻole wale ia e hoʻoikaika i kā mākou mau kumu makemakika a me ke kino akā wehe pū i ka puka i kahi ākea o nā noi loea a me ka ʻepekema holomua.
