Question

What is the cross product of `[1, 3, 4]` and `[3, 7, 9]`?

Answer 1

The vector is `=〈-1,3,-2〉`

Explanation:

The cross product of 2 vectors is

`| (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=〈1,3,4〉` and `vecb=〈3,7,9〉`

Therefore,

`| (veci,vecj,veck), (1,3,4), (3,7,9) |`

`=veci| (3,4), (7,9) | -vecj| (1,4), (3,9) | +veck| (1,3), (3,7) |`

`=veci(3*9-4*7)-vecj(1*9-4*3)+veck(1*7-3*3)`

`=〈-1,3,-2〉=vecc`

Verification by doing 2 dot products

`〈-1,3,-2〉.〈1,3,4〉=-1*1+3*3-2*4=0`

`〈-1,3,-2〉.〈3,7,9〉=-1*3+3*7-2*9=0`

So,

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