Question

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

Answer 1

The andwer is `=〈8,-7,-26〉`

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=〈2,6,-1〉` and `vecb=〈3,-4,2〉`

Therefore,

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

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

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

`=〈8,-7,-26〉=vecc`

Verification by doing 2 dot products

`〈8,-7,-26〉.〈2,6,-1〉=8*2-6*7+26*1=0`

`〈8,-7,-26〉.〈3,-4,2〉=8*3+7*4-26*2=0`

So,

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