Question

What is the cross product of `[0,8,5]` and `[1, 4, -2]`?

Answer 1

The vector is `=〈-36,5,-8〉`

Explanation:

The cross product is a vector perpendiculat to 2 other vectors

`| (veci,vecj,veck), (d,e,f), (g,h,i) |`

where `〈d,e,f〉` and `〈g,h,i〉` are the 2 vectors

Here, we have `veca=〈0,8,5〉` and `vecb=〈1,4,-2〉`

Therefore,

`| (veci,vecj,veck), (0,8,5), (1,4,-2) |`

`=veci| (8,5), (4,-2) | -vecj| (0,5), (1,-2) | +veck| (0,8), (1,4) |`

`=veci(-2*8-5*4)-vecj(-2*0-5*1)+veck(0*4-8*1)`

`=〈-36,5,-8〉=vecc`

Verification by doing 2 dot products

`〈-36,5,-8〉.〈0,8,5〉=-36*0+5*8-5*8=0`

`〈-36,5,-8〉.〈1,4,-2〉=-36*1+5*4+2*8=0`

So,

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