Question

What is the cross product of `<-3 ,-6 ,-3 >` and `<-2 ,1 , -7 >`?

Answer 1

The vector is `=〈45,-15,-15〉`

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=〈-3,-6,-3〉` and `vecb=〈-2,1,-7〉`

Therefore,

`| (veci,vecj,veck), (-3,-6,-3), (-2,1,-7) |`

`=veci| (-6,-3), (1,-7) | -vecj| (-3,-3), (-2,-7) | +veck| (-3,-6), (-2,1) |`

`=veci(-6*-7+3*1)-vecj(-3*-7-3*2)+veck(-3*1-6*2)`

`=〈45,-15,-15〉=vecc`

Verification by doing 2 dot products

`〈45,-15,-15〉.〈-3,-6,-3〉=-45*3+6*15+3*15=0`

`〈45,-15,-15〉.〈-2,1,-7〉=-45*2-15*1+15*7=0`

So,

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