Question

What is the cross product of `[2, 4, 5]` and `[2, -5, 8]`?

Answer 1

The vector is `=〈57,-6,-18〉`

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=〈2,4,5〉` and `vecb=〈2,-5,8〉`

Therefore,

`| (veci,vecj,veck), (2,4,5), (2,-5,8) |`

`=veci| (4,5), (-5,8) | -vecj| (2,5), (2,8) | +veck| (2,4), (2,-5) |`

`=veci((4)*(8)-(5)*(-5))-vecj((1)*(3)-(1)*(1))+veck((-1)*(1)-(2)*(1))`

`=〈57,-6,-18〉=vecc`

Verification by doing 2 dot products

`〈57,-6,-18〉.〈2,4,5〉=(57)*(2)+(-6)*(4)+(-18)*(5)=0`

`〈57,-6,-18〉.〈2,-5,8〉=(57)*(2)+(-6)*(-5)+(-18)*(8)=0`

So,

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