Qalabka Isku-dhufashada Isdhaafsiga ah iyadoo la adeegsanayo Qaybaha Vektor- ka Cutubka
Waxaan si toos ah u xisaabin karnaa badeecada isdhaafka ah haddii aan naqaanno qaybaha vector-ka. Habraacu waa isku mid sida badeecada dhibcaha . Marka hore, waxaan ku dhufannaa vector-yada cutubka i , j , iyo k . Badeecada vector-ka ee u dhaxaysa vector-yada cutubka isku midka ah waa eber.
i x i = j x j = k x k = 0
Iyadoo la tixraacayo isla'egta isku dhufashada vector-ka ee hore loo soo saaray (A x B = AB dembi θ) iyo hantida ka hortagga isku-dhafka ee isku-dhufashada vector-ka (A x B = - B x A), ka dibna waxaan helnaa:
i x j = -j x i = k
j x k = -k x j = i
k x i = – i x k = j
Hadda waxaan ku muujineynaa vektorrada A iyo B marka loo eego qaybahooda, waxaan burburineynaa badeecadooda oo waxaan isticmaaleynaa badeecada vektorrada cutubyada.
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)
Sababtoo ah 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, sidaas darteed:
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 B 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
Haddii C = A x B markaas qaybaha C waa sidan soo socota:
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
