Ko te hua whakawhiti o ngā whārite e rua, hei tauira, ngā whārite A me B, ka tuhia ko A x B ( A whakawhiti B ). Ka kiia te hua whakawhiti he hua 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.
Ka pēhea mēnā ka hurihia e tātou a A x B ki a B x A?
Tuatahi, ka tuhia e tātou ngā whārite B me A me ngā wāhanga o te 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; me whakatau tātou i tōna ahunga. Hei whakatau i te ahunga o A x B , ka tuhia tuatahitia e tātou ngā whārite A me B e ai ki te whakaaturanga i raro nei. Ka whakatakotoria ēnei whārite e rua ki runga 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
He poutū te ahunga o C ki te papa e takoto ana ngā whārite A me B. Ka taea e tātou te whakamahi i te ture ringa-matau hei whakatau i te ahunga o C. Ki te pupuri tātou i ō tātou maihao ki te ahunga whakamuri, ko te ahunga o C kei 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 mātou ngā whārite B me A e whakaaturia ana i raro nei. Ka whakanohoia ēnei whārite e rua ki roto i tētahi papa.
Mena C = B x A māka C = BA sin teta.
He poutū te ahunga o C ki te papa e takoto ana ngā whārite B me A. Ka taea e tātou te whakamahi i te ture ringa-matau hei whakatau i te ahunga o C. Ki te pupuri tātou i ō tātou maihao ki te ahunga karaka, ka rite te ahunga o C ki te ahunga o te koromatua e anga ana ki raro.
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 o B i A x B he ritenga kē ki te ahunga o B i B x A.
2. Mena he poutū ngā whārite e rua tetahi ki tetahi , ko te koki i hangaia ko 90 ° . Sin 90 ° = 1. Nō reira, ko te rahi o te hua whakawhiti i waenga i ngā whārite A me B ka puta penei:
A x B = AB hara theta = AB hara 90 o = AB
B x A = BA sin theta = BA sin 90 o = BA
3. Mena kei te ahunga kotahi ngā whārite e rua, ko te koki i hangaia ko te 0 o.
Sin 0 o = 0. Nō reira, ko te uara o te hua whakawhiti i waenga i ngā whārite A me B ka puta penei.
A x B = AB hara theta = AB hara 0 o = 0
B x A = BA sin theta = BA sin 0 o = 0
