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)` ?

Let vec(a),vec(b)andvec(c) be three non-coplanar vectors and let vec(p),vec(q),vec(r) be the vectors defined by the relations 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)])" Then the value of "(vec(a)+vec(b))*vec(p)+(vec(b)+vec(c))*vec(q)+(vec(c)+vec(a))*vec(r)=

If vec(a),vec(b),vec(c) are the non-coplanar vectors, then (vec(a).vec(b)xxvec(c))/(vec(c)xxvec(a).vec(b))+(vec(b).vec(a)xxvec(c))/(vec(c).vec(a)xxvec(b))= ……………

If [vec(a),vec(b),vec(c)]=1, then the value of (vec(a)*(vec(b)xxvec(c)))/((vec(c)xxvec(a))*vec(a))+(vec(b)*(vec(c)xxvec(a)))/((vec(a)xxvec(b))*vec(c))+(vec(c)(vec(a)xxvec(b)))/((vec(c)xxvec(b))*vec(a)) is

If vec(a),vec(b),vec(c) are coplanar vectors, show that (vec(a)xxvec(b))xx(vec(c)xxvec(d))=vec(0)

If vec(d)=vec(a)xx(vec(b)xxvec(c))+vec(b)xx(vec(c)xxvec(a))+vec(c)xx(vec(a)xxvec(b))," then "