Question

What is the cross product of `<8, 4 ,-2 >` and `<-1, -4, 1>`?

Answer 1

The answer is `=〈-4,-6,-28〉`

Explanation:

The cross product of 2 vectors is calculated with the determinant

`| (veci,vecj,veck), (d,e,f), (g,h,i) |`

where `〈d,e,f〉` and `〈g,h,i〉` are the 2 vectors

Here, we have `veca=〈8,4,-2〉` and `vecb=〈-1,-4,1〉`

Therefore,

`| (veci,vecj,veck), (8,4,-2), (-1,-4,1) |`

`=veci| (4,-2), (-4,1) | -vecj| (8,-2), (-1,1) | +veck| (8,4), (-1,-4) |`

`=veci(4-8)-vecj(8-2)+veck(-32+4)`

`=〈-4,-6,-28〉=vecc`

Verification by doing 2 dot products

`〈-4,-6,-28〉.〈8,4,-2〉=-32-24+56=0`

`〈-4,-6,-28〉.〈-1,-4,1〉=4+24-28=0`

So,

`vecc` is perpendicular to `veca` and `vecb`