Maʻi lele. hou o vectors

I ka like o ka makemakika hiki aku ai i kekahi mau enrichment a me ka ulu i loko o ka likeʻole ma o ka mea a me na mea paahana no ka hōʻikeʻia nani? Aneieʻike manaʻo. Ke'ī mai, i ka palena manawa o ka manaʻo o ka hele mai i laupaʻi characterization o ke kaiapuni, me ka hou papa o geometrical huahelu loaa e wehewehe mai i keʻano o ko lākou mau 'ano apau loa. Akā, me ka hooulu ana o maoli sciences a me ka makemakika iho noi e noi mai ana i ka hoike a me ka hoʻopaʻa 'ana i ka mea hou, a ka pukaʻana hōʻikeʻia nani i na mea paahana. Ma kekahi, he nui helu o physical mea hiki ole ke wehewehe aku wale ma ka helu, no ka mea, mea nui, a me ka olelo o ko lākou mau hana. A no ka mea, ka mea i kauoha ia Hoʻohana i emi iho a me nāʻaoʻao, me ka laulā nā loina, a laila, ma luna o kēia kumu, a ua huli i ka hou manaʻo o ka makemakika - maʻi lele manaʻo.

Hana walaʻauʻana makemakika ana ma luna o ia mau mea, hoi, ho'ākāka 'ia ma ka physical kumu, a me keia e ho'ōla alakaʻi i ka hoʻokumuʻo o ka maʻi lele hōʻailona helu, a e hāpai i ka nui kūlana i loko o ke kahua o ke kino ai' theories. I ka Ia manawa, i ka makemakika, i kēiaʻano o ka hōʻailona helu a me kona generalizations ua lilo i ka loa i ka pono 'ōlelo, e like me ka mea o ka loaa a me nä hou hopena.

He aha mea he maʻi lele?

Maʻi lele o ka 'ia paha o nā mea a pau i kauoha ia laina Hoʻohana nei ke ao hookahi loa, a me ka hoʻoholo ma mua ao ao. Kēlā me kēia no ka Hoʻohana o keia kau i kapa ia maʻi lele kiʻi.

Ua mea akaka i ka maʻi lele ua denoted ma kona kiʻi. All kuhikuhi Hoʻohana, i ho i ka maʻi lele, i ka like loa a me ka ao ao i ka poe i kaheaia, niioaaonoaaiii, i ka lōʻihi (Module loa waiwai) a me ka ao ao o ka maʻi lele. Kona lōʻihi ua hōʻikeʻia e IAI. Mau vectors i mai la ia e like ina ka mea, i ka mea e like me mamua, a me ka ia loa.

Kuhikuhi laina Hoʻohana nona ka hoʻomaka 'wahi o A, a me ka hopena - ke wahi B, ua uniquely wehewehe aku ma ka kauoha paʻa o nā kumu i (A; B). E noonoo oe i ka ai iiiaanoaa o ka hui (A, A), (B; C) .... Kēia 'ia paha ho i ka maʻi lele i ua kapaia' Aʻohe a denoted 0. Ke kiʻi o ka 'Aʻohe maʻi lele o kekahi wahi. Module Aʻohe maʻi lele ua manaoia e e Aʻohe. I ka manaʻo o ka 'Aʻohe maʻi lele ao ao ua ole kona manao.

No kekahi ole-Aʻohe maʻi lele ua nānā ', haawiia i ke ku pono, a laila kekahi a i ka ia lōʻihi akā, e ku pono ana ka ao ao. Vectors i i ka ia paha e ku pono anaʻaoʻao, kapa collinear.

I ka manawa kūpono o ka hoʻohana 'ana i nā vectors pili me ka hoʻokomo' ia 'o ka hana ma luna o vectors a me ka hana ana o ka maʻi lele hōʻailona helu, a he nui kona waiwai i loko o like me ka mea mau "helu" hōʻailona helu (eia nae, o ka papa, ma laila nō i nuiʻokoʻa).

Hou o na vectors elua (collinear) ua hana ia e ka triangle rula (kau i ka kumu o ka maʻi lele e ma ka hope o ka maʻi lele i, laila, i ka maʻi lele i + e hoʻohuiʻia nā luna o ka maʻi lele i kekahi, mai ka maʻi lele hopena b) 'ole kekahi parallelogram (i hoʻomaka' vectors i ka a me ka e ma kekahi wahi, a laila maʻi lele i + e, me ka hoʻomaka ma ka ia wahi, o he diagonal o ka parallelogram, a ua kūkulu i ka vectors i kekahi, a b). Hou o vectors (he mau) hiki ke hana ma ka hoʻohana 'ana i ka rula o ka iieeaii. Inā nā hua'ōlelo i collinear, e hoemiia ka lakou mau geometric? Ieoaeunoaa iauaeoia.

i hoemi ana me ka vectors mea i hoakaka ia wahi, i ka ana me ka nui: hou o vectors - hou o kūpono wahi, e laʻa me, ina he = (x1, y1) a me ka e = (X2; y2), a laila, he + a b = (x1 + X2 ; y1 + y2).

Nō kāu maʻi lele hou i nā mea a pau i ka algebraic ka waiwai i mea hoʻomaopop 'ana i ka hou nui:

1. By permutation puu dala ua ole hoʻololi:
   he + a b = e + i ka
   Hou o vectors me keia waiwai ma hope mai o ka parallelogram rula. Ua, aha mea i ke koena unuhi i loko o ka mea e hōʻuluʻulu i nā vectors i ka a me ka b, ina ka diagonal o ka parallelogram mea no ka ia?
2. I ka waiwai o ka associativity:
   (A + b) + pela aku = i + (b + c).
3. Ohui i ka maʻi lele o ka 'Aʻohe maʻi lele' aʻole e hoʻololi i kekahi mea:
   he +0 = he
   Ua maopopo ina ua manao kekahi triangle me ka hou ana o ke kuanaʻike akau.
4. Kēlā me kēia maʻi lele i kekahi i ka mea ku pono maʻi lele, denoted ma - he; maʻi lele Eia hou, 'oluʻolu a me ka io, e like me' Aʻohe: He + (- he) = 0.