Kayan ninkaya ta amfani da kayan haɗin kai Vektor na Naúrar
Za mu iya ƙididdige samfurin giciye kai tsaye idan mun san abubuwan da ke cikin vectors. Tsarin iri ɗaya ne da samfurin digoDa farko dai, muna yin ninkawa tsakanin vectors na naúrar. i, j dan kSamfurin vector tsakanin vectors naúrar guda ɗaya sifili ne.
i x i = j x j = k x k = 0
Ta hanyar komawa ga lissafin ninka vector da aka samo a baya (A x B = AB zunubi θ) da kuma kadarar hana tafiye-tafiye ta ninka vector (A x B = - B x A), sannan mu samu:
i x j = -j x i = k
j x k = -k x j = i
k x i = -i x k = j
Yanzu mun bayyana vector ɗin A dan B cikin abubuwan da ke cikinsa, yana wargaza yawansa da kuma amfani da ninka yawan vectors na na'urarsa.
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)
Domin i x i = j x j = k x k = 0 dan i x j = -j x i = k, j x k = -k x j = i, k x i = -i x k = j, haka:
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
Idan C = A x B sannan sassan C sune kamar haka:
Cx = AyBz - AzBy
Cy = AzBx - Ax Bz
Cz = AxBy - AyBx
