Question

What is the cross product of `<7, 2 ,6 >` and `<-3 ,5 ,-6 >`?

Answer 1

The vector is `=〈-42,24,41〉`

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=〈7,2,6〉` and `vecb=〈-3,5,-6〉`

Therefore,

`| (veci,vecj,veck), (7,2,6), (-3,5,-6) |`

`=veci| (2,6), (5,-6) | -vecj| (7,6), (-3,-6) | +veck| (7,2), (-3,5) |`

`=veci((2)*(-6)-(6)*(5))-vecj((7)*(-6)-(6)*(-3))+veck((7)*(5)-(2)*(-3))`

`=〈-42,24,41〉=vecc`

Verification by doing 2 dot products

`〈-42,24,41〉.〈7,2,6〉=(-42)*(7)+(24)*(2)+(41)*(6)=0`

`〈-42,24,41〉.〈-3,5,-6〉=(-42)*(-3)+(24)*(5)+(41)*(-6)=0`

So,

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