Oloa fa'alava e fa'aaoga ai vaega vector iunite

Mea Fa'atelega Fa'alava e Fa'aaogaina ai Vaega Veketo o le Iunite

E mafai ona tatou fuafuaina sa'o le cross product pe afai tatou te iloa vaega o vectors. E tutusa le faiga ma le dot product . Muamua, tatou te fa'ateleina unit vectors i , j , ma le k . O le vector product i le va o unit vectors tutusa e zero.

i x i = j x j = k x k = 0

I le faasino i le fua faatatau o le faateleina o vector na maua muamua (A x B = AB agasala θ) ma le meatotino e tete'e i le fesuia'iga o fa'atelega veketo (A x B = – B x A), ona tatou maua lea:

i x j = -j x i = k

j x k = -k x j = i

k x i = – i x k = j

O lea la ua tatou faʻaalia vectors A ma le B i tulaga o a la vaega, vaevaeina a la oloa ma faʻaaoga le oloa o vectors iunite.

A x B= (A_xi + A_yj + A_zk) x (B_xi + B_yj + B_zk)

A x B = A_xi x B_xi + A_xi x B_yj + A_xi x B_zk +

A_yj x B_xi + A_yj x B_yj + A_yj x B_zk +

A_zk x B_xi + A_zk x B_yj + A_zk x B_zk

A x B = A_xB_x (i x i) + A_xB_y (i x j) + A_x B_z (i x k) +

A_yB_x (j x i) + A_yB_y (j x j) + A_yB_z (j x k) +

A_zB_x (k x i) + A_zB_y (k x j) + A_zB_z (k x k)

Karena i x i = j x j = k x k = 0 Tanu i x j = –j x i = k,  j x k = –k x j = i, k x i = -i x k = j, o lea la:

A x B = A_xB_x (0) + A_xB_y (k+ A_x B_z (-j+

A_yB_x (-k+ A_yB_y (0) + A_yB_z (i+

A_zB_x (j+ A_zB_y (-i+ A_zB_z (0)

A x B = A_xB_y (k+ A_x B_z (-j+

A _y B _x ( -k ) + A _y B _z ( i ) +

A _z B _x ( j ) + A _z B _y ( -i )

A x B = A_xB_y (k+ A_x B_z (-j+ A_yB_x (-k+ A_yB_z (i+ A_zB_x (j+ A_zB_y (-i)

A x B = (A_yB_z - A_zB_y)i + (A_zB_x - A_x B_z)j + (A_xB_y - A_yB_x )k

Afai o le C = A x B o vaega ia o le C e faapea:

_Cx = A _y B _z – A _z B _y

_Cy = A _z B _x – A _x B _z

_Cz = A _x B _y – A _y B _x