Question

What is the cross product of `[3,2, 5]` and `[1,2,-4]`?

Answer 1

The cross product is `=〈-18,17,4〉`

Explanation:

Let the vectors be `veca=〈a_1,a_2,a_3〉` and `vecb=〈b_1,b_2,b_3〉`

The cross product is given by
`veci` `color(white)(aaaa)` `vecj` `color(white)(aaaa)` `veck`
`a_1` `color(white)(aaaaa)` `a_2` `color(white)(aaaa)` `a_3`
`b_1` `color(white)(aaaaa)` `b_2` `color(white)(aaaa)` `b_3`

`=〈a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1〉`

With the vectors `〈3,2,5〉` and `〈1,2,-4〉`
we get the cross product `〈-8-10,12+5,6-2〉`
`=〈-18,17,4〉`