Question

How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors `<4,0,=2>times<-7,1,0>`?

Answer 1

The vector is `〈2,14,4〉`

Explanation:

The cross product of `〈4,0,-2〉xx〈-7,1,0〉` is

`veci` `color(white)(aa)` `vecj` `color(white)(aa)` `veck`
`4` `color(white)(aaa)` `0` `color(white)(aa)` `-2`
`-7` `color(white)(aa)` `1` `color(white)(aaa)` `0`

cross product `=` `(veci(0+2)+vecj(-(0-14))+veck(4-0))`

`=〈2,14,4〉`
To check this we do the dot products

`〈2,14,4〉`.`〈4,0,-2〉` `=8+0-8=0`

`〈2,14,4〉` `〈-7,1,0〉` `=-14+14+0=0`

As the dot products are `=0`
So the 3 vectors are perpendicular