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)=`

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) ?

If vec a, vec b, vec c are three non-coplanar vectors and vec p, vec q, vec r are vectors defined by the relations vec p = (vec b xxvec c) / ([vec avec bvec c]), vec q = (vec c xxvec a) / ([vec avec bvec c]), vec r = (vec a xxvec b) / ([vec avec bvec c]) then the value of expression (vec a + vec b) * vec p + (vec b + vec c) * vec q + (vec c + vec a) * vec r is equal to

Let veca , vecb, vec c be three non coplanar vectors , and let vecp , vecq " and " vec r be the vectors defined by the relation vecp = (vecb xx vec c )/([veca vecb vec c ]), vec q = (vec c xx vec a)/([veca vecb vec c ]) " and " vec r = (vec a xx vec b)/([veca vecb vec c ]) Then the value of the expension (vec a + vec b) .vec p + (vecb + vec c) .q + (vec c + vec a) . vec r is equal to

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

Let vec(p),vec(q),vec(r) be three unit vectors such that vec(p)xxvec(q)=vec(r) . If vec(a) is any vector such that [vec(a)vec(q)vec(r )]=1,[vec(a)vec(r)vec(p )]=2 , and [vec(a)vec(p)vec(q )]=3 , then vec(a)=

If vec a,vec b, and vec c are three non-coplanar vectors,then find the value of (vec a*(vec b xxvec c))/(vec b*(vec c xxvec a))+(vec b*(vec c xxvec a))/(vec c*(vec a xxvec b))+(vec c*(vec b xxvec a))/(vec a xxvec c))

If vec a,vec b,vec c be any three non-zero non coplanar vectors and vectors vec p=(vec b xx vec c)/(vec a.vec b xx vec c),vec q=(vec c xx vec a)/(vec a.vec b xx vec c) vec r=(vec a xx vec b)/(veca.vec b xx vec c), then [vec p vec q vec r] equals -