Question

What is the cross product of `[2, -1, 4]` and `[5, 2, -2]`?

Answer 1

`<2,-1,4> xx <5,2,-2> = <-6,24,9>`

Explanation:

We can use the notation:

`\ \ \ \ \ ( (2),(-1),(4) ) xx ( (5),(2),(-2) ) = | (ul(hat(i)),ul(hat(j)),ul(hat(k))), (2,-1,4),(5,2,-2) |`

`" " = | (-1,4),(2,-2) | ul(hat(i)) - | (2,4),(5,-2) | ul(hat(j)) +| (2,-1),(5,2) | ul(hat(k))`

`" " = (2-8) ul(hat(i)) - (-4-20) ul(hat(j)) +(4+5) ul(hat(k))`

`" " = -6 ul(hat(i)) +24 ul(hat(j)) +9 ul(hat(k))`
`" " = ( (-6),(24),(9) )`