A = {8,9,10 } and B = {1,2,3 }, determine n(AxB)
AxB = | i j k |
| 8 9 10 |
| 1 2 3 |
AxB = (9*3 – 10*2)i - (8*3 – 10*1)j + (8*2 – 9*1)k
AxB = (27 – 20)i - (24 – 10)j + (16 – 9)k
AxB = 7i - 14j + 7k = 7{i - 2j + k} = 7{1,-2,1}
The cross product for AxB is evaluated like the determinant for a 3x3 square matrix. For example ...
M = | a b c |
| d e f |
| g h i |
Det(M) = a(ei – fh) – b(di – f g) + c(dh – eg)