Question

What is the cross product of `[3, 2, 5]` and `[4,3,6]`?

Answer 1

The vector is `=〈-3,2,1〉`

Explanation:

The vector perpendicular to 2 vectors is calculated with the determinant (cross product)

`| (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=〈3,2,5〉` and `vecb=〈4,3,6〉`

Therefore,

`| (veci,vecj,veck), (3,2,5), (4,3,6) |`

`=veci| (2,5), (3,6) | -vecj| (3,5), (4,6) | +veck| (3,2), (4,3) |`

`=veci(-3)-vecj(-2)+veck(1)`

`=〈-3,2,1〉=vecc`

Verification by doing 2 dot products

`veca.vecc`

`=〈3,2,5>.〈-3,2,1〉=-9+4+5=0`

`vecb.vecc`

`=〈4,3,6〉.〈-3,2,1〉=-12+6+6=0`

So,

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