` vec a , vec ba n d vec c` are three non-coplanar vectors and ` vec r` is any arbitrary vector. Prove that `[ vec b vec c vec r] vec a+[ vec c vec a vec r] vec b+[ vec a vec b vec r] vec c=[ vec a vec b vec c] vec rdot`

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

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

[vec a + vec b, vec b + vec r * vec cvec c + vec a] = 2 [vec with bvec c]

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =

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

If vec a, vec b, vec c are coplanar vectors, then | vec a, vec b, vec cvec b, vec c, vec avec b, vec a, vec b] | = vec a

If vec a,vec b, and vec c are three non-coplanar non-zero vecrtors,then prove that (vec a*vec a)vec b xxvec c+(vec a*vec b)vec c xxvec a+(vec a*vec c)vec a xxvec b=[vec bvec cvec a]vec a

If vec a, vec b, vec c are three non-Coplanar nonzero vectors then (vec a * vec a) vec b xxvec c + (vec a * vec b) vec c xxvec a + (vec a * vec c) vec a xxvec ba is equal to