Question

What is the cross product of `<-2, 5 ,-2 >` and `<7 ,3 ,2 >`?

Answer 1

The vector is `=〈16,-10,-41〉`

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=〈-2,5,-2〉` and `vecb=〈7,3,2〉`

Therefore,

`| (veci,vecj,veck), (-2,5,-2), (7,3,2) |`

`=veci| (5,-2), (3,2) | -vecj| (-2,-2), (7,2) | +veck| (-2,5), (7,3) |`

`=veci((5)*(2)-(-2)*(3))-vecj((-2)*(2)-(-2)*(7))+veck((-2)*(3)-(5)*(7))`

`=〈16,-10,-41〉=vecc`

Verification by doing 2 dot products

`〈16,-10,-41〉.〈-2,5,-2〉=(16)*(-2)+(-10)*(5)+(-41)*(-2)=0`

`〈16,-10,-41〉.〈7,3,2〉=(16)*(7)+(-10)*(3)+(-41)*(2)=0`

So,

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