Zinthu Zochulukitsa Pogwiritsa Ntchito Zigawo Vekitala ya Unit
Tikhoza kuwerengera chinthu chosakanikirana mwachindunji ngati tikudziwa zigawo za ma vector. Dongosolo lake ndi lofanana ndi chinthu cha donthoChoyamba, timachita kuchulukitsa pakati pa ma vector a unit. i, j dani kChogulitsa cha vekitala pakati pa mavekitala a unit imodzi 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 kuchulukitsa 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 tikunena za vekitala A dani B mu zigawo zake, kugawa kuchuluka kwake ndikugwiritsa ntchito kuchulukitsa kwa ma vector ake 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+
AyBx (-k+ AyBz (i+
AzBx (j+ AzBy (-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 kenako zigawo za C ndi izi:
Cx = AyBz - AzBy
Cy = AzBx - Ax Bz
Cz = AxBy - AyBx
