The cross product of 2 vectors is a vector perpendicular to the 2 vectors. It 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=〈4,5,-9〉 and vecb=〈5,-3,-3〉
Therefore,
| (veci,vecj,veck), (4,5,-9), (5,-3,-3) |
=veci| (5,-9), (-3,-3) | -vecj| (4,-9), (5,-3) | +veck| (4,5), (5,-3) |
= veci (5*-3--3*-9) - vecj (4*-3-5*-9) + veck (4*-3-5*5)
=〈-42,-33,-37〉=vecc
Verification by doing 2 dot products
〈-42,-33,-37〉.〈4,5,-9〉=-42*4-33*5+37*9=0
〈-42,-33,-37〉.〈5,-3,-3〉=-42*5+33*3+37*3=0
So,
vecc is perpendicular to veca and vecb
