Lisebelisoa tsa ho Atisa ka Tšepe tse Sebelisang Likarolo tsa Vector ea Yuniti
Re ka bala sehlahisoa se kopaneng ka kotloloho haeba re tseba likarolo tsa li-vector. Mokhoa o ts'oana le oa sehlahisoa sa matheba . Taba ea pele, re atisa li-vector tsa yuniti i , j , le k . Sehlahisoa sa vector pakeng tsa li-vector tsa yuniti e le 'ngoe ke lefela.
i x i = j x j = k x k = 0
Ka ho bua ka equation ea katiso ea vector e nkiloeng pele (A x B = AB ntle θ) le thepa e khahlanong le phetoho ea ho atisa vector (A x B = - B x A), ebe re fumana:
i x j = -j x i = k
j x k = -k x j = i
k x i = – i x k = j
Jwale re hlahisa divekthara A le B mabapi le dikarolo tsa tsona, re qhaqha sehlahiswa sa tsona mme re sebedisa sehlahiswa sa divekthara tsa yuniti.
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)
Hobane i x i = j x j = k x k = 0 dan tao i x j = -j x i = k, j x k = -k x j = i, k x i = -i x k = j, kahoo:
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
Haeba C = A x B joale likarolo tsa C ke tse latelang:
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
