Question

What is the cross product of `<9,2,8 >` and `<6, -2, 7 >`?

Answer 1

The vector is `= <30,-15,-30>`

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=〈9,2,8〉` and `vecb=〈6,-2,7〉`

Therefore,

`| (veci,vecj,veck), (9,2,8), (6,-2,7) |`

`=veci| (2,8), (-2,7) | -vecj| (9,8), (6,7) | +veck| (9,2), (6,-2) |`

`=veci((2)*(7)-(8)*(-2))-vecj((9)*(7)-(8)*(6))+veck((9)*(-2)-(2)*(6))`

`=〈30,-15,-30〉=vecc`

Verification by doing 2 dot products

`〈30,-15,-30〉.〈9,2,8〉=(30)*(9)+(-15)*(2)+(-30)*(8)=0`

`〈30,-15,-30〉.〈6,-2,7〉=(30)*(6)+(-15)*(-2)+(-30)*(7)=0`

So,

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