Question

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

Answer 1

`<<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) )`