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〉#
