Zinthu Zochulukitsa Pogwiritsa Ntchito Zigawo za Vector
Tikhoza kuwerengera chinthu chodutsana mwachindunji ngati tikudziwa zigawo za mavekitala. Njirayi ndi yofanana ndi ya chinthu cha dot . Choyamba, timachulukitsa mavekitala a unit i , j , ndi k . Chinthu cha vekitala pakati pa mavekitala a unit yomweyo ndi zero.
i x i = j x j = k x k = 0
Poganizira za equation yochulukitsa mavekitala yomwe idachokera kale (A x B = AB tchimo θ) ndi mphamvu yotsutsana ndi kusintha kwa kuchuluka kwa vekitala (A x B =- B x A), kenako timapeza:
i x j = -j x i = k
j x k = -k x j = i
k x i = – i x k = j
Tsopano tikuwonetsa ma vector A ndi B malinga ndi zigawo zawo, kuwononga zinthu zawo ndikugwiritsa ntchito zomwe zapangidwa ndi ma vector a unit.
A x B= (Axi + Ayj + Azk) x (Bxi + Byj + Bzk)
A x B = Axi x Bxi + Axi x Byj + Axi x Bzk +
Ayj x Bxi + Ayj x Byj + Ayj x Bzk +
Azk x Bxi + Azk x Byj + Azk x Bzk
A x B = AxBx (i x i) + AxBy (i x j) + Ax Bz (i x k) +
AyBx (j x i) + AyBy (j x j) + AyBz (j x k) +
AzBx (k x i) + AzBy (k x j) + AzBz (k x k)
Chifukwa i x i = j x j = k x k = 0 dani i x j =-j x i = k, j x k =-k x j = i, k x i = -i x k = j, kotero:
A x B = AxBx (0) + AxBy (k+ Ax Bz (-j+
AyBx (-k+ AyBy (0) + AyBz (i+
AzBx (j+ AzBy (-i+ AzBz (0)
A x B = AxBy (k+ Ax Bz (-j+
A y B x ( -k ) + A y B z ( i ) +
A z B x ( j ) + A z By y ( -i )
A x B = AxBy (k+ Ax Bz (-j+ AyBx (-k+ AyBz (i+ AzBx (j+ AzBy (-i)
A x B = (AyBz - AzBy)i + ((AzBx - Ax Bz)j + ((AxBy - AyBx )k
Ngati C = A x B ndiye kuti zigawo za C ndi izi:
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
