What is the cross product of #<7, 2 ,5 ># and #<-3 ,1 ,-6 >#?

1 Answer
Steve M
Dec 24, 2016

# <<7,2,5>> xx <<-3,1,-6 >> = <<-17,27,13>> #

Explanation:

We can use the notation:
# ( (7),(2),(5) ) xx ( (-3),(1),(-6) ) = | (ul(hat(i)),ul(hat(j)),ul(hat(k))), (7,2,5),(-3,1,-6) |#

# " " = | (2,5),(1,-6) | ul(hat(i)) - | (7,5),(-3,-6) | ul(hat(j)) +| (7,2),(-3,1) | ul(hat(k)) #

# " " = {(2)(-6)-(1)(5)} ul(hat(i)) #
# " " - {(7)(-6)-(-3)(5)} ul(hat(j)) " #
# " " + {(7)(1)-(-3)(2)} ul(hat(k)) #

# " " = (-12-5) ul(hat(i)) - (-42+15) ul(hat(j)) +(7+6) ul(hat(k))#

# " " = -17 ul(hat(i)) +27 ul(hat(j)) +13 ul(hat(k)) #
# " " = ( (-17),(27),(13) ) #

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