A = {8,9,10 } and B = {1,2,3 }, determine n(AxB)

Question

Let A = {8,9,10,} and B = {1,2,3 ], determine n(AxB)Find the indicated product.

Answer 1

If A and B are rectangular vectors, then we can write:

A=8i+9j+10k and B=i+2j+3k 

The right-hand rule is:

X-product of unit vectors	i	j	k
i	0	k	-j
j	-k	0	i
k	j	-i	0

Their cross-product A X B=

{8,9,10}{1,2,3}=-9k+10j+16k-20i-24j+27i=(7)i+(-14)j+(7)k={7,-14,7}=7(1,-2,1) or -7(-1,2,-1).

Answer 2

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)