Question

What is the cross product of `[1, 3, 4]` and `[2, -5, 8]`?

Answer 1

The vector is `=〈44,0,-11〉`

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=〈1,3,4〉` and `vecb=〈2,-5,8〉`

Therefore,

`| (veci,vecj,veck), (1,3,4), (2,-5,8) |`

`=veci| (3,4), (-5,8) | -vecj| (1,4), (2,8) | +veck| (1,3), (2,-5) |`

`=veci(44)-vecj(0)+veck(-11)`

`=〈44,0,-11〉=vecc`

Verification by doing 2 dot products

`veca.vecc`

`=〈1,3,4>.〈44,0,-11〉=44-44=0`

`vecb.vecc`

`=〈2,-5,8〉.〈44,0,-11〉=88-88=0`

So,

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