Question

What is the cross product of `[1, -2, -3]` and `[3, 7, 9]`?

Answer 1

The vector is `=〈3,-18,13〉`

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=〈1,-2,-3〉` and `vecb=〈3,7,9〉`

Therefore,

`| (veci,vecj,veck), (1,-2,-3), (3,7,9) |`

`=veci| (-2,-3), (7,9) | -vecj| (1,-3), (3,9) | +veck| (1,-2), (3,7) |`

`=veci((-2)*(9)-(-3)*(7))-vecj((1)*(9)-(-3)*(3))+veck((1)*(7)-(-2)*(3))`

`=〈3,-18,13〉=vecc`

Verification by doing 2 dot products

`〈3,-18,13〉.〈1,-2,-3〉=(3)*(1)+(-18)*(-2)+(13)*(-3)=0`

`〈3,-18,13〉.〈3,7,9〉=(3)*(3)+(-18)*(7)+(13)*(9)=0`

So,

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