Nā Veka like: Nā Veka like
I ka makemakika a me ke kino, he mau mea nui nā vectors i hoʻohana ʻia e hōʻike i nā nui me ka nui a me ke kuhikuhi. Mai nā noi maʻalahi e like me ka hoʻoholo ʻana i ke kūlana ma ka lewa a hiki i nā moʻo hana paʻakikī i ka dynamics fluid, ua komo ka manaʻo o nā vectors i nā lālā like ʻole o ka ʻepekema. ʻO kahi manaʻo nui e hoʻomaopopo ai, ʻo ia nā vectors like, a i ʻole, ka vector like.
Ke Hoʻomaopopo nei i nā Vectors
Ma mua o ko kākou ʻimi ʻana i ke kumumanaʻo o nā vectors like me ka hohonu, e hoʻomaka kākou ma ka hoʻomaopopo ʻana i ke ʻano o kahi vector. ʻO ka vector kahi mea makemakika i hōʻike ʻia e kahi pua nona nā ʻano kumu ʻelua: ka nui (a i ʻole ka lōʻihi) a me ke kuhikuhi. No ka laʻana, hiki ke hōʻike ʻia ka ikaika, ka wikiwiki, a me ke kahua uila ma ke ʻano he vectors.
Ma ke ʻano makemakika, hiki ke hōʻike ʻia kahi vector ma nā ana ʻelua ma ke ʻano he \((x, y)\), kahi ʻo \(x\) a me \(y\) nā ʻāpana o ka vector ma nā axis \(x\) a me \(y\). Ma nā ana ʻekolu, ua hōʻike ʻia kahi vector ma ke ʻano he \((x, y, z)\).
Nā Vectors like
Ua manaʻo ʻia nā vectors he like a like paha inā he like ko lākou nui a me ke kuhikuhi. Hiki ke ʻokoʻa nā kūlana hoʻomaka (huelo) a me ka hopena (poʻo), akā inā like ko lākou lōʻihi a me ke kuhikuhi, ua ʻōlelo ʻia lākou he like. No ka laʻana, ʻelua mau vectors \(\vec{A} = (3, 4)\) a me \(\vec{B} = (3, 4)\) i ʻelua mau ana ua ʻōlelo ʻia he like no ka mea like kā lākou mau ʻāpana, a hōʻike lākou i nā vectors like ma ke ʻano o ka lōʻihi a me ke kuhikuhi.
Pehea e hoʻoholo ai i nā Vectors like
No ka hoʻoholo ʻana inā like nā vectors ʻelua, hiki iā mākou ke hahai i kekahi mau ʻanuʻu maʻalahi:
1. E nānā i nā ʻāpana:
E nānā inā like nā ʻāpana \(x\) a me \(y\) (a i ʻole \(z\) ma nā ana ʻekolu) o nā vectors ʻelua. Inā like kēia mau ʻāpana, a laila like nā vectors.
2. E nānā i ka nui:
Pono nā vectors like e like ka nui. Ua helu ʻia ka nui o kahi vector \(\vec{A} = (x, y)\) ma nā ana ʻelua e ke ʻano:
\[
|\vec{A}| = \sqrt{x^2 + y^2}
\]
Ma nā ana ʻekolu, penei ke ʻano:
\[
|\vec{A}| = \sqrt{x^2 + y^2 + z^2}
\]
3. E nānā i ke kuhikuhi:
ʻOiai he mea kākaʻikahi i loko o ka pōʻaiapili o nā vectors mua, aia kekahi mau kūlana kahi e loaʻa ai i nā vectors ʻelua nā kuhikuhi ʻē aʻe akā like ka nui. Eia nō naʻe, pili pinepine kēia me ka manaʻo o kahi 'vector maikaʻi ʻole', kahi e kūʻē ai nā kuhikuhi akā like nā nui.
Ma ka hahai ʻana i kēia mau ʻanuʻu, hiki iā mākou ke hōʻoia i like nā vectors ʻelua a mākou e hoʻohālikelike nei.
Nā Hana me nā Vectors like
ʻO ka hoʻomaopopo ʻana he like maoli nā vectors like ʻole e hiki ai iā mākou ke hoʻomaʻalahi i nā hana makemakika like ʻole. Eia kekahi mau hana vector kumu a me ko lākou hopena no nā vectors like:
1. Hoʻohui Vector:
Hana ʻia ka hoʻohui vector ma ka hoʻohui ʻana i kā lākou mau ʻāpana pili. Inā \(\vec{A} = (x_1, y_1)\) a me \(\vec{B} = (x_2, y_2)\), a laila ʻo ka hopena o ka hoʻohui ʻana:
\[
\vec{A} + \vec{B} = (x_1 + x_2, y_1 + y_2)
\]
Pili nō hoʻi kēia i nā vectors like; inā like nā vectors ʻelua ma mua o ka hoʻohui ʻana, e like nō nā hopena.
2. Ka Hoʻemi Vector:
Ua like loa ka hana hoʻemi me ka hoʻohui ʻana, kahi e unuhi ai mākou i nā ʻāpana kūpono:
\[
\vec{A} – \vec{B} = (x_1 – x_2, y_1 – y_2)
\]
3. Hoʻonui Scalalar:
Ke hoʻonui ʻia kahi vector \(\vec{A}\) me kahi scalar \(k\), ʻo ka hopena:
\[
k \vec{A} = (kx, ky)
\]
ʻO ka loli scalar i loko o kahi vector like e hoʻopuka i kahi vector e like ana ma ka unahi a me ke kuhikuhi.
Nā Laʻana o ke Ao Maoli
He mea pono loa ke kumumanaʻo o nā vectors like i nā ʻano noi like ʻole o ke ao maoli. No ka laʻana, i ka physics, hiki ke hōʻike ʻia nā ikaika e hana ana ma kahi mea e nā vectors. ʻElua mau ikaika o ka nui like a me ke kuhikuhi like, ʻoiai inā e hana ana ma nā wahi like ʻole, e loaʻa ka hopena like i ka neʻe ʻana o ka mea.
Pēlā nō, i ka ʻepekema kamepiula a me nā kiʻi kamepiula, hoʻohana ʻia nā vectors e kuhikuhi i ke kūlana a me nā loli i ka lewa. Manaʻo pinepine nā algorithms e hilinaʻi nei i nā hoʻololi vector e hiki ke hoʻololi ʻia nā vectors like kekahi i kekahi me ka ʻole o ka hoʻololi ʻana i ka hopena hope loa.
Ka hopena
ʻO ka hoʻomaopopo ʻana i ke kumumanaʻo o nā vectors like, a i ʻole ka vector like, he mea nui ia i nā ʻano aʻo ʻepekema he nui. Ua like nā vectors ʻelua inā he like ko lākou nui a me ke kuhikuhi, me ka nānā ʻole i ko lākou mau wahi hoʻomaka a i ʻole nā wahi hopena. ʻO ka ʻike ʻana a me ka ʻimi ʻana i kēia kumumanaʻo e hoʻomaʻalahi i nā hana makemakika, ka loiloi kino, a me nā noi i ka ʻenehana.
Me kēia ʻike, ʻaʻole mākou e aʻo wale i nā helu makemakika akā loaʻa pū kekahi ʻike hohonu i ke ʻano o ka hopena o nā hōʻike vector i ka nānā ʻana a me ka hoʻoponopono ʻana i nā pilikia maoli like ʻole. ʻO ka ʻike o nā vectors like e lawelawe ana ma ke ʻano he kahua e hoʻoikaika ai i ke kahua makemakika a he noi ākea a ʻano like ʻole i nā ʻano aʻo like ʻole.
