Rauemi Whakarea Ira Mā te Whakamahi i ngā Wāhanga Waehere Ira
Ka taea e tātou te tatau tika i te hua tauine mēnā e mōhio ana tātou ki ngā wāhanga x, y me z o ngā whārite A me B (ngā whārite e mōhiotia ana).
Hei mahi i tētahi hua ira pēnei, ka mahi tuatahi mātou i tētahi hua ira o ngā whārite waeine, kātahi ka whakaatu i ngā whārite A me B ki roto i ō rāua wāhanga, ka wetewete i te hua, ā, ka whakamahi i te hua o ngā whārite waeine.
He poutū ngā whārite waeine i , j, me k tetahi ki tetahi, kia māmā ake ai ngā tataunga. Mā te whakamahi i te whārite whakarea tauine i ahu mai i runga ake nei ( AB = AB cos theta ), ka whiwhi tātou:
i. i = j. j = k. k = (1)(1) cos 0 = 1
i.j = i.k = j.k = (1)(1) cos 90 o = 0
Inaianei ka whakaatuhia e mātou ngā whārite A me B e ai ki ō rāua wāhanga, ka wetewetehia tō rāua hua, ā, ka whakamahia te hua o ngā whārite kotahi.
A . B = Axi . Bxi + Axi . Byj + Axi . Bzk +
Ayj . Bxi + Ayj . Byj + Ayj . Bzk +
Azk . Bxi + Azk . Byj + Azk . Bzk
A . B = AxBx (i . i) + AxBy (i . j) + Ax Bz (i . k) +
AyBx (j . i) + AyBy (j . j) + AyBz (j . k) +
AzBx (k . i) + AzBy (k . j) + AzBz (k . k)
Na te mea i . i = j . j = k . k = 1 me i . j = i . k = j . k = 0, kātahi:
A . B = AxBx (1) + AxBy (0) + Ax Bz (0) +
AyBx (0) + AyBy (1) + AyBz (0) +
AzBx (0) + AzBy (0) + AzBz (1)
A. B = A x B x ( 1) + 0 + 0 +
0 + A y B y (1) + 0 +
0 + 0 + A z B z (1)
A . B = AxBx + AyBy + AzBz
I runga i ngā hua o tēnei tataunga, ka taea te whakatau ko te hua tauine, te hua ira rānei o ngā whārite e rua, ko te tapeke o ngā hua o ō rāua wāhanga ōrite.
Tauira Pātai 1:
Wetere nui A dan B ko te 5 me te 4 ia, e whakaaturia ana i te ahua i raro nei. Ko te koki i hangaia ko te 90oTatauhia hua ira ngā wetere e rua.
Kōrero
I mua i te tatau i te hua ira o ngā whārite A me B, me mōhio tuatahi tātou ki ngā wāhanga o te whārite tuarua.
A x = (5) cos 0 o = (5) (1) = 5
A y = (5) hara 0 o = (5) (0) = 0
A z = 0
B x = (4) cos 90 o = (4) (0) = 0
B y = (4) hara 90 o = (4) (1) = 4
Bz = 0
Ko ngā wāhanga wāhanga anake kei te tuaka-x o te whārite A , ā, ko ngā wāhanga wāhanga anake kei te tuaka-y o te whārite B. Kore te wāhanga z nā te mea kei roto ngā whārite A me B i te papa xy.
Nā, ka tatauhia e tātou te hua ira i waenga i ngā whārite A me B mā te whakamahi i te whārite hua ira me ngā whārite wāhanga:
A. B = Ax Bx + AyBy + AzBz
A. B = (5) (0) + (0) (4) + 0
A. B = 0 + 0 + 0
A. B = 0
Me whakarite ki te tikanga tuatahi
AB = AB cos theta
AB = (4)(5) cos 90
AB = (4) (5) (0)
AB = 0
He rite tonu te hua.
Tauira Pātai 2:
Wetere nui A dan B e 5 me te 4 ia, e whakaaturia ana i te pikitia i raro nei. Tātaihia hua ira ngā whārite e rua, mēnā ko te koki i hangaia he 30o
Kōrero
I mua i te tatau i te hua ira o ngā whārite A me B, me mōhio tuatahi tātou ki ngā wāhanga o te whārite tuarua.
Kore te wāhanga z nā te mea kei roto ngā whārite A me B i te papa xy.
Nā, ka tatauhia e tātou te hua ira i waenga i ngā whārite A me B mā te whakamahi i te whārite hua ira me ngā whārite wāhanga:
Whakatauritea ki te tikanga tuatahi.
