If A,B,C,D are any four points in space prove that `vec(AB)xxvec(CD)+vec(BC)xvec(AD)+vec(CA)xxvec(BD)=2vec(AB)xxvec(CA)`

If A,B,C,D are four points in space, then |vec(AB)xvec(CD)+vec(BC)xxvec(AD)+vec(CA)xxvec(BD)|=k (are of /_\ABC) where k= (A) 5 (B) 4 (C) 2 (D) none of these

A,B,C,D are any four points,prove that vec AB*vec CD+BC*vec AD+vec CA*vec BD=0

A,B,C and D are any four points in the space,then prove that |vec AB xxvec CD+vec BC xxvec AD+vec CA xxvec BD|=4 (area of o+ABC.)

Prove that (vec b xxvec c) xx (vec c xxvec a) = [vec with bvec c] vec c

Prove that [vec b xxvec cvec c xxvec with a xxvec b] = [vec with bvec c] ^ (2)

If vectors b,c and d are not coplanar,then prove that vector (vec a xxvec b)xx(vec c xxvec d)+(vec a xxvec c)xx(vec d xxvec b)+(vec a xxvec d)xx(vec b xxvec c) is parallel to vec a .

If vec a + vec b + vec c = o, prove that vec a xxvec b = vec b xxvec c = vec c xxvec a

Let vec a,vec b, and vec c be any three vectors,then prove that [vec a xxvec bvec b xxvec cvec c xxvec a]=[vec avec bvec c]^(2)

If vec a,vec b,vec c are three non-coplanar non-zero vectors and vec r is any vector in space, then (vec a xxvec b)xx(vec r xxvec c)+(vec b xxvec c)xx(vec r xxvec a)+(vec c xxvec a)xx(vec r xxvec b) is equal to