Question

What is the cross product of `<7 ,4 ,-3 >` and `<-5 ,2 , -7 >`?

Answer 1

The vector is `=〈-22,64,34〉`

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=〈7,4,-3〉` and `vecb=〈-5,2,-7〉`

Therefore,

`| (veci,vecj,veck), (7,4,-3), (-5,2,-7) |`

`=veci| (4,-3), (2,-7) | -vecj| (7,-3), (-5,-7) | +veck| (7,4), (-5,2) |`

`=veci((4)*(-7)-(-3)*(2))-vecj((7)*(-7)-(-3)*(5))+veck((7)*(2)-(-5)*(4))`

`=〈-22,64,34〉=vecc`

Verification by doing 2 dot products

`〈-22,64,34〉.〈7,4,-3〉=(-22)*(7)+(64)*(4)+(34)*(-3)=0`

`〈-22,64,34〉.〈-5,2,-7〉=(-22)*(-5)+(64)*(2)+(34)*(-7)=0`

So,

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