Question

What is the cross product of `<9,2,8 >` and `<1,3,-4 >`?

Answer 1

The vector is `=〈-32,44,25〉`

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=〈9,2,8〉` and `vecb=〈1,3,-4〉`

Therefore,

`| (veci,vecj,veck), (9,2,8), (1,3,-4) |`

`=veci| (2,8), (3,-4) | -vecj| (9,8), (1,-4) | +veck| (9,2), (1,3) |`

`=veci(-2*4-3*8)-vecj(-9*4-8*1)+veck(9*3-2*1)`

`=〈-32,44,25〉=vecc`

Verification by doing 2 dot products

`〈-32,44,25〉.〈9,2,8〉=-32*9+44*2+25*8=0`

`〈-32,44,25〉.〈1,3,-4〉=-32*1+44*3-4*25=0`

So,

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