Question

What is the cross product of `<< -3,-6,-3 >>` and `<< -5,2,-7 >>`?

Answer 1

The vector is `=〈48,-6,-36〉`

Explanation:

The cross product of 2 vectors is calculated with the determinant

`| (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=〈-3,-6,-3〉` and `vecb=〈-5,2,-7〉`

Therefore,

`| (veci,vecj,veck), (-3,-6,-3), (-5,2,-7) |`

`=veci| (-6,-3), (2,-7) | -vecj| (-3,-3), (-5,-7) | +veck| (-3,-6), (-5,2) |`

`=veci((-6*-7)-(2*-3))-vecj((-3*-7)-(-5*-3))+veck((-3*2)-(-6*-5))`

`=〈48,-6,-36〉=vecc`

Verification by doing 2 dot products (inner products)

`〈48,-6,-36〉.〈-3,-6,-3〉=-48*3+6*6+36*3=0`

`〈48,-6,-36〉.〈-5,2,-7〉=-48*5-6*2+36*7=0`

So,

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