Te hua whakawhiti o ngā whākapū e rua, hei tauira te whākapū A dan B i tuhia hei A x B (A silang B). Ka kiia te whakarea whakawhiti he whakarea whārite nā te mea ka puta he rahinga whārite i te hua o tēnei whakarea.
Hei tauira, he rite te āhua o te whārite A me te whārite B ki te ahua i raro nei.
Hei tautuhi i te hua whakawhiti i waenga i ngā whārite A dan B (A x B), ka tuhia e mātou te irahiko A dan B e whakaaturia ana i te pikitia i runga ake nei, ā, kua whakaaturia hoki ngā wāhanga vector He poutū a B ki a A, he ōrite ki a B sin theta.
Nō reira, ka taea e tātou te tautuhi i te rahi o te hua whakawhiti o ngā whārite. A dan B (A x B) hei hua o te rahi o te ira A me ngā wāhanga whārite B poutū ki te whārite A.
Ā, mēnā A x B kua hoki tātou ki te noho B x A ?
Tuatahi, me tuhi he wetereo B dan A me ngā wāhanga whārite A e poutū ana ki a B
I runga i tēnei pikitia, ka taea e tātou te tautuhi i te hua whakawhiti i waenga i ngā whārite B dan A (B x A) hei hua o te rahi o te ira B me ngā wāhanga whārite A poutū ki te whārite B. I tuhia mā te pāngarau:
Te Aronga o te Whakareatanga Whakawhiti A x B
He hua whārite te hua whakawhiti, nō reira he rahi me te ahunga te hua. Kua tangohia te rahi o te hua whārite i runga ake nei; whakatauhia tōna ahunga. Hei whakatau i te ahunga A x B, tuatahi ka tuhia e mātou ngā whārite A me B e whakaaturia ana i raro nei. Ka whakanohoia ēnei whārite e rua ki roto i tētahi papa.
Whakareatanga whakawhiti A x B kua tautuhia hei whārite poutū ki te papa e noho ana te whārite A dan B kei reira. He rite te rahi ki AB hara tit. Mēnā C = A x B māka C = AB hara tit
Āra C poutū ki te papa e noho ana te ira A dan B kei reira. Ka taea e tātou te whakamahi i te ture ringa matau hei whakatau i te ahunga C. Ki te pupuri tātou i ō tātou maihao ki tētahi ahunga e rerekē ana ki te ahunga o te hurihanga karaka, ko te ahunga C i te ahunga kotahi me te koromatua e anga whakarunga ana.
Te Aronga o te Whakareatanga Whakawhiti B x A
Hei whakatau i te ahunga B x A, tuatahi ka tuhia e tātou he whārite B dan A pērā i te pikitia i raro nei. Ka whakanohoia ēnei whārite e rua ki roto i te papa.
Mena C = B x A māka C = BA sin teta.
He poutū te ahunga o C ki te paparangi kei reira te whārite B dan A kei reira. Ka taea e tātou te whakamahi i te ture ringa matau hei whakatau i te ahunga C. Ki te pupuri tātou i ō tātou maihao i te ahunga e rite ana ki te ahunga o te hurihanga o ngā ringa ki te taha matau, ko te ahunga C rite tonu ki te ahunga o te koromatua e anga whakararo ana.
A x B kāore i te ōrite ki B x A. Ko te hua o te hua whakawhiti he rahinga wetereo, haunga te rahinga, he ahunga anō hoki. I te maturuturunga i runga ake nei, ko te ahunga A x B te taha whakamuri ki B x A.
Ko ētahi mea e pā ana ki te whakarea whakawhiti me mōhio koe:
1. He ārai-whakawhiti te whakarea whakawhiti.
A x B = – B x A
Ko te tohu kino e tohu ana ko te ahunga B I te A x B te taha whakamuri B I te B x A.
2. Mena he motuhake ngā whārite e rua tegak lurus kātahi ka 90 te koki i hangaiao. Hara 90o = 1. Nō reira, ko te rahi o te hua whakawhiti i waenga i ngā whārite A dan B ka penei te āhua:
A x B = AB hara tit = AB hara 90o = AB
B x A = BA hara tit = BA hara 90o = BA
3. Mena kei te ahunga kotahi ngā whārite e rua, ko te koki i hangaia he 0o.
Hara 0o = 0. Nō reira, ko te uara o te hua whakawhiti i waenga i ngā whārite A dan B ka puta mai penei.
A x B = AB hara teta = AB sin 0o = 0
B x A = BA hara teta = BA sin 0o = 0
