Question

What is the cross product of `<3,-6,4>` and `<-1,-1,2>`?

Answer 1

`<3,-6,4> xx <-1,-1,2> = <-8,-10,-9>`

Explanation:

We can use the notation:

`\ \ \ \ \ ( (3),(-6),(4) ) xx ( (-1),(-1),(2) ) = | (ul(hat(i)),ul(hat(j)),ul(hat(k))), (3,-6,4),(-1,-1,2) |`

`" " = | (-6,4),(-1,2) | ul(hat(i)) - | (3,4),(-1,2) | ul(hat(j)) +| (3,-6),(-1,-1) | ul(hat(k))`

`" " = (-12-(-4)) ul(hat(i)) - (6-(-4)) ul(hat(j)) +(-3-6) ul(hat(k))`

`" " = -8 ul(hat(i)) - 10 ul(hat(j)) - 9 ul(hat(k))`
`" " = ( (-8),(-10),(-9) )`