Ka huahana kea o ʻelua vectors, no ka laʻana vector A a hiki B i kākau ʻia e like me A x B (A silang B). Ua kapa ʻia ka hoʻonui kea he hoʻonui vector no ka mea ʻo ka hopena o kēia hoʻonui ʻana e hua mai i kahi nui vector.
Eia kekahi laʻana, ua like ke ʻano o ka vector A a me ka vector B me ke kiʻi ma lalo nei.
No ka wehewehe ʻana i ka huahana kea ma waena o nā vectors A a hiki B (A x B), kahakiʻi mākou i ka vector A a hiki B e like me ka mea i hōʻike ʻia ma ke kiʻi ma luna, a ua hōʻike pū ʻia nā ʻāpana vector He kū pololei ʻo B iā A, ʻo ia hoʻi ua like me B sin theta.
No laila, hiki iā mākou ke wehewehe i ka nui o ka huahana kea o nā vectors. A a hiki B (A x B) ma ke ʻano he huahana o ka nui o ka vector A me nā ʻāpana vector B kū pololei i ka vector A.
He aha inā A x B ua hoʻi mākou i ke ʻano B x A ?
ʻO ka mea mua, e kahakiʻi kākou i kahi vector B a hiki A a me nā ʻāpana vector A ʻo ia hoʻi ke kū pololei iā B
Ma muli o kēia kiʻi, hiki iā mākou ke wehewehe i ka huahana kea ma waena o nā vectors B a hiki A (B x A) ma ke ʻano he huahana o ka nui o ka vector B me nā ʻāpana vector A kū pololei i ka vector B. I kākau ʻia ma ka makemakika:
Ke kuhikuhi o ka hoʻonui ʻana i ke keʻa A x B
He huahana vector ka huahana cross, no laila he nui a he kuhikuhi ka huahana. Ua loaʻa ka nui o ka huahana vector ma luna; i kēia manawa e hoʻoholo i kona kuhikuhi. No ka hoʻoholo ʻana i ke kuhikuhi A x B, ke kahakiʻi mua nei mākou i nā vectors A a me B e like me ka mea i hōʻike ʻia ma lalo nei. Hoʻonoho mākou i kēia mau vectors ʻelua i loko o kahi mokulele.
Hoʻonui kea A x B ua wehewehe ʻia he vector kū pololei i ka mokulele kahi e kū ai ka vector A a hiki B aia. Ua like ka nui me AB hewa ʻanakēInā C = A x B Maka C = AB hewa ʻanakē
ʻAra C kū pololei i ka mokulele kahi i loaʻa ai ka vector A a hiki B aia. Hiki iā mākou ke hoʻohana i ke kānāwai lima ʻākau e hoʻoholo ai i ke kuhikuhi CInā paʻa kākou i ko kākou mau manamana lima i kahi kuhikuhi e kūʻē ana i ke kuhikuhi o ka wili ʻana o ka uaki, a laila ke kuhikuhi C ma ke kuhikuhi like me ka manamana nui e kuhikuhi ana i luna.
Ke kuhikuhi o ka hoʻonui ʻana i ke keʻa B x A
No ka hoʻoholo ʻana i ke kuhikuhi B x A, ke kahakiʻi mua nei mākou i kahi vector B a hiki A e like me ke kiʻi ma lalo nei. Hoʻonoho mākou i kēia mau vectors ʻelua i loko o kahi mokulele.
Ina C = B x A Maka C = BA me ka ʻole o ka ʻaina.
ʻO ke kuhikuhi o C ua kū pololei i ka mokulele kahi i loaʻa ai ka vector B a hiki A aia. Hiki iā mākou ke hoʻohana i ke kānāwai lima ʻākau e hoʻoholo ai i ke kuhikuhi CInā paʻa kākou i ko kākou mau manamana lima i kahi kuhikuhi e kūlike ana me ke kuhikuhi o ka wili ʻana o nā lima ma ka ʻaoʻao uaki, a laila ke kuhikuhi C e like me ke kuhikuhi ʻana o ka manamana nui e kuhikuhi ana i lalo.
A x B ʻaʻole like me B x A. ʻO ka hopena o ka huahana kea i kahi nui vector, ʻoiai ʻaʻole i loaʻa ka nui, loaʻa pū kekahi kuhikuhi. Ma ka hāʻule ʻana ma luna, kuhikuhi A x B ʻaoʻao ʻē aʻe i B x A.
ʻO kekahi mau mea e pili ana i ka hoʻonui kea e pono ai ʻoe e ʻike:
1. He anti-commutative ka hoʻonui kea.
A x B = - B x A
Hōʻike ka hōʻailona maikaʻi ʻole i ke kuhikuhi B ma A x B ʻaoʻao ʻē aʻe B ma B x A.
2. Inā kūʻokoʻa kekahi i kekahi nā vectors ʻelua kū pololei a laila ʻo ke kihi i hoʻokumu ʻia he 90o. Hewa 90o = 1. No laila, ʻo ka nui o ka huahana kea ma waena o nā vectors A a hiki B e like me kēia:
A x B = AB hewa ʻanakē = AB hewa 90o = AB
B x A = BA hewa ʻanakē = BA hewa 90o = BA
3. Inā like ke kuhikuhi o nā vectors ʻelua, a laila ʻo ke kihi i hoʻokumu ʻia he 0o.
Hewa 0o = 0. No laila, ʻo ka waiwai o ka huahana kea ma waena o nā vectors A a hiki B e ʻike ʻia penei.
A x B = AB hewa theta = AB sin 0o = 0
B x A = BA hewa theta = BA sin 0o = 0
