Let `vec(a), vec(b), vec(c)` be non-coplanar vectors and `vec(p)=(vec(b)xxvec(c))/([vec(a)vec(b)vec(c)]), vec(q)=(vec(c)xxvec(a))/([vec(a)vec(b)vec(c)]), vec(r)=(vec(a)xxvec(b))/([vec(a)vec(b)vec(c)])`.
What is the value of
`(vec(a)-vec(b)-vec(c)).vec(p)+(vec(b)-vec(c)-vec(a)).vec(q)+(vec(c)-vec(a)-vec(b)).vec(r)` ?