Te Mārama ki ngā Wētera Waeine
Ko te ira waeine he ira ko tōna rahi ko te 1. Kāore he ira o te ira waeine, ā, ko tana mahi he tohu i te ahunga i te wāhi. Hei wehewehe i a ia mai i te ira noa, ka tāia ki te momotuhi matotoru (mō te tuhinga kua tāia) ka tāpirihia rānei he tohu ^ ki runga ake (mō te tuhituhi ā-ringa).
I roto i te pūnaha taunga Cartesian (xyz) ka whakamahia e mātou te ira waeine i hei tohu i te ahunga o te tuaka-x pai, j hei tohu i te ahunga o te tuaka-y pai, k hei tohu i te ahunga o te tuaka-y pai.
Ngā Wāhanga Wetereo
Hei whakamāmā ake i te mārama, whakaarohia te tauira e whai ake nei. Hei tauira, he whārite F kei reira e whakaaturia ana i te ahua i raro nei.
I roto i te pikitia, ko te ine ira i e whakaatu ana i te ahunga o te tuaka-x pai me j e tohu ana i te ahunga o te tuaka-y pai. Ka taea e tātou te kī i te whanaungatanga i waenganui i wāhanga wetere me ō rātou wāhanga, penei:
Fx = Fx x i
F y = F y j
Ka taea e tātou te tuhi i te whārite F i roto i ōna wāhanga penei:
F = F x i + F y j
Hei tauira, e rua ngā whārite, arā, ko A me B i roto i te pūnaha taunga xy, ā, ka whakaatuhia ēnei whārite e rua i runga i ō rāua wāhanga:
A = A x i + A y j
B = B x i + B y j
A, mehemea ka tāpirihia a A me B ?
R = A + B
R = ((Axi + Ayj) + (Bxi + Byj)
R = ((Ax + Bx)i + ((Ay + By)j
R = R x i + R y j
Mena kāore ngā whārite katoa e noho ana i te papa xy, ka taea e tātou te tāpiri i tētahi whārite kotahi k, e tohu ana i te ahunga o te tuaka-z pai.
A = A x i + A y j + A z k
B = B x i + B y j + B z k
Mena ka tāpirihia ngā whārite A me B , ka puta ngā hua e whai ake nei:
R = A + B
R = ((Axi + Ayj + Azk) + (Bxi + Byj + Bzk)
R = ((Ax + Bx)i + ((Ay + By)j + ((Az + Bz)k
R = R x i + R y j + R z k
