Ehara ngā tau whārite i te tau noa, nō reira kāore e taea te whakamahi tika i te whakarea noa ki a rātou. Me whakamahi tātou i te whakarea whārite. E rua ngā momo whakarea whārite: te whakarea ira me te whakarea whakawhiti. Ka kiia hoki te whakarea ira he whakarea tauine nā te mea ka puta he rahinga tauine. Ka kiia hoki te whakarea whakawhiti he whakarea whārite nā te mea ka puta he rahinga whārite. Hei tauira, e rua ngā whārite, arā A dan BTe whakareatanga tauine o ngā whārite A dan B i kīia me AB KNā te mea e whakamahia ana te tohu ira e te arena, ka kiia tēnei whakareatanga hua iraTe whakareatanga o te pūwero A dan B i kīia me A x BNā te mea e whakamahi ana i te tuhipoka x, kātahi ka kiia tēnei whakareatanga ko te whakareatanga whakawhiti.
Hei tauira, i te hoatutanga o te vector A dan B e whakaaturia ana i te ahua i raro nei. Ko te hua ira i waenga i ngā whārite A dan B i tuhia hei AB (A pūwāhi B).
Hei tautuhi i te hua ira o ngā whārite A dan B (AB), te tohu whakaahua A me ngā whārite Nā ye hanga ana i tētahi koki θ. Muri iho ka tuhia e mātou te whakaaturanga o te ira B te ahunga o te irahiko A. He wāhanga tēnei whakaaturanga o te whārite B e whakarara ana ki te whārite A, he rite te rahi ki B cos θ.
Nō reira, ka tautuhia e mātou AB hei wetere nui A whakareatia ki ngā wāhanga whārite B e whakarara ana ki A. Mā te pāngarau ka taea e tātou te tuhi penei:
AB cos θ he tau noa (tauine). Nō reira, ka kiia hoki te hua ira ko te hua tauine. Me pēhea mēnā ko te hua ira i waenga i ngā whārite A dan B whakahurihia ki BA i mua i tā tātou tautuhi BA, tuatahi ka tuhia e mātou te whakaaturanga o te ira A ki ngā wetereo B (tirohia te ahua i raro nei).
I runga i tēnei whakaahua, ka taea e tātou te tautuhi BA hei wetere nui B whakareatia ki ngā wāhanga whārite A e whakarara ana ki B. Mā te pāngarau ka taea e tātou te tuhi penei:
Hua hua ira AB = AB cos θ me te hua o te hua ira BA = BA cos θNā te mea AB cos θ = BA cos θ, kātahi ka pā AB = BA
Ko ētahi mea e pā ana ki te whakarea ira me mōhio koe:
1. E tutuki ana i te hua ira te ture tauwhitiwhiti.
AB = BA
2. Ka tutuki i te hua ira te ture tohatoha.
A. (B + C) = AB + AC
3. Mena he poutū ngā whārite A me B tetahi ki tetahi, ko te hua ira AB = 0
Ina te wetereti A dan B poutū tetahi ki tetahi, kātahi ko te koki i hangaia he 90o. Kos 90o = 0. Nō reira: AB = AB cos tit = AB whaimana 90o = 0. I tētahi atu taha, BA = BA cos tit = BA whaimana 90o = 0
4. Mena kei te ahunga kotahi te whārite A me te whārite B , ko AB = AB cos 0 o = AB
Ina te wetereti A dan B i te ahunga kotahi, kātahi ko te koki i hangaia ko te 0o. Ko te 0 = 1. Nō reira, AB = AB cos tit = AB whaimana 0o = AB. Engari BA = BA cos tit = BA whaimana 0o = BA
(Kaua koe e pōhēhē ki AB dan BANui AB = nui BAHei tauira, ko te rahi o te whārite A = 2. te rahi o te whārite B = 3. kātahi AB = 2.3 = 6; he rite tonu tēnei ki BA = 3.2 = 6.
5. Tētahi atu āhuatanga mō ngā whārite e rua i te ahunga kotahi, ki te mea ko A = B ka whiwhi tātou i te AA = A 2 , BB = B 2 rānei
6. Mena kei ngā ahunga rerekē ngā whārite A me B (ina kei ngā ahunga rerekē ngā whārite e rua, ko te koki i hangaia he 180º) , ko te hua o te whakarea AB = AB cos 180º = AB (-1) = -AB.
Cos 180º = -1.
Tauira raruraru:
E 4 ngā waeine o te rahi o te whārite A , ā, e 3 ngā waeine o te rahi o te whārite B. Tātaihia te hua ira o ngā whārite e rua mēnā ko ngā koki i hangaia e ngā whārite e rua he 60º, 90º me te 180º.
Kōrero
Nā te mea ko AB = BA , ka taea e tātou te whiriwhiri ki te whakamahi i tētahi o ēnei. Hei tauira, ka whakamahia e tātou a AB
AB = AB cos theta
Ko te rahi o A = 4 ngā waeine, ā, ko te rahi o B = 3 ngā waeine.
