The vector perpendicular to 2 vectors is calculated with the determinant (cross product)
| (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=〈29,-35,-17〉 and vecb=〈0,41,31〉
Therefore,
| (veci,vecj,veck), (29,-35,-17), (0,41,31) |
=veci| (-35,-17), (41,31) | -vecj| (29,-17), (0,31) | +veck| (29,-35), (0,41) |
=veci(-35*31+17*41)-vecj(29*31+17*0)+veck(29*41+35*0)
=〈-388,-899,1189〉=vecc
Verification by doing 2 dot products
〈-388,-899,1189〉.〈29,-35,-17〉=-388*29+899*35-17*1189=0
〈-388,-899,1189〉.〈0,41,31〉=-388*0-899*41+1189*31=0
So,
vecc is perpendicular to veca and vecb
The unit vector in the direction of vecc is
=vecc/||vecc||
||vecc||=sqrt(388^2+899^2+1189^2)=sqrt2372466
The unit vector is =1/1540.3〈-388,-899,1189〉
