Question

What is the cross product of `(2i -3j + 4k)` and `(4 i + 4 j + 2 k)`?

Answer 1

The vector is `=〈-22,12,20〉`

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,-3,4〉` and `vecb=〈4,4,2〉`

Therefore,

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

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

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

`=〈-22,12,20〉=vecc`

Verification by doing 2 dot products

`〈-22,12,20〉.〈2,-3,4〉=(-22)*(2)+(12)*(-3)+(20)*(4)=0`

`〈-22,12,20〉.〈4,4,2〉=(-22)*(4)+(12)*(4)+(20)*(2)=0`

So,

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