Ua kākau ʻia ka huahana kea o nā vectors ʻelua, no ka laʻana nā vectors A a me B, ʻo A x B ( A kea B ). Ua kapa ʻia ka huahana kea he huahana 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 e hoʻolilo kākou iā A x B i B x A?
ʻO ka mea mua, kahakiʻi mākou i nā vectors B a me A a me nā ʻāpana o ka vector A e kū pololei ana 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 kea, no laila he nui a he kuhikuhi ka hopena. Ua loaʻa ka nui o ka huahana vector ma luna; i kēia manawa pono mākou e hoʻoholo i kona kuhikuhi. No ka hoʻoholo ʻana i ke kuhikuhi o A x B , kahakiʻi mua 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 ma 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
ʻO ke kuhikuhi o C ua kū pololei i ka mokulele kahi e waiho ai nā vectors A a me B. Hiki iā kākou ke hoʻohana i ke kānāwai lima ʻākau e hoʻoholo ai i ke kuhikuhi o C. Inā paʻa kākou i ko kākou mau manamana lima ma ke kuhikuhi ʻākau, a laila aia ke kuhikuhi o 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 ʻo B x A , kahakiʻi mua mākou i nā vectors B a me A e like me ka mea i hōʻike ʻia 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 e moe ai nā vectors B a me A. Hiki iā kākou ke hoʻohana i ke kānāwai lima ʻākau e hoʻoholo ai i ke kuhikuhi o C. Inā paʻa kākou i ko kākou mau manamana lima ma ke kuhikuhi ʻākau, a laila ua like ke kuhikuhi o C me ke kuhikuhi 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.
ʻA x B = – B x A
Hōʻike ka hōʻailona maikaʻi ʻole ua kūʻē ke kuhikuhi o B ma A x B i ke kuhikuhi o B ma B x A.
2. Inā kū pololei nā vectors ʻelua kekahi i kekahi , ʻo ke kihi i hoʻokumu ʻia he 90 o . Sin 90 o = 1. No laila, e ʻike ʻia ka nui o ka huahana kea ma waena o nā vectors A a me B penei:
A x B = AB sin theta = AB sin 90 o = AB
B x A = BA sin theta = BA sin 90 o = BA
3. Inā like ke kuhikuhi o nā vectors ʻelua, a laila ʻo ke kihi i hoʻokumu ʻia he 0 o.
Sin 0 o = 0. No laila, e ʻike ʻia ka waiwai o ka huahana kea ma waena o nā vectors A a me B penei.
A x B = AB sin theta = AB sin 0 o = 0
B x A = BA sin theta = BA sin 0 o = 0
