I understand that when we apply the Lagrange's identity onto the expression we can get 0. However, in terms of geometry, the expression add 3 vectors starting from each vertex with the same direction as the altitude going across that vertex. Why the sum of these 3 vectors is the 0 vector, as we don't know the angle between them and I'm not sure the relation between their length....

keenan

@yingxiul Here's one explanation though I don't find it particularly clear! Would love to see someone write up a (much) simpler version of this explanation, with nice pictures. ;-)

I understand that when we apply the Lagrange's identity onto the expression we can get 0. However, in terms of geometry, the expression add 3 vectors starting from each vertex with the same direction as the altitude going across that vertex. Why the sum of these 3 vectors is the 0 vector, as we don't know the angle between them and I'm not sure the relation between their length....

@yingxiul Here's one explanation though I don't find it particularly clear! Would

loveto see someone write up a (much) simpler version of this explanation, with nice pictures. ;-)