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

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Answer 1 · 2016-12-24T01:01:20

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

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

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

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

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

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

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