Question

What is the cross product of `[2, -1, 1]` and `[3,-6,4]`?

Answer 1

The vector is `=〈2,-5,-9〉`

Explanation:

The cross product of 2 vectors is calculated with the determinant

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

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

Here, we have `veca=〈2,-1,1〉` and `vecb=〈3,-6,4〉`

Therefore,

`| (veci,vecj,veck), (2,-1,1), (3,-6,4) |`

`=veci| (-1,1), (-6,4) | -vecj| (2,1), (3,4) | +veck| (2,-1), (3,-6) |`

`=veci((-1)*(4)-(-6)*(1))-vecj((2)*(4)-(1)*(3))+veck((2)*(-6)-(-1)*(3))`

`=〈2,-5,-9〉=vecc`

Verification by doing 2 dot products

`〈2,-5,-9〉.〈2,-1,1〉=(2)*(2)+(-5)*(-1)+(-9)*(1)=0`

`〈2,-5,-9〉.〈3,-6,4〉=(2)*(3)+(-5)*(-6)+(-9)*(4)=0`

So,

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