If `vec a,vec b` and `vec c` are three non-zero vectors,prove that `[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]`

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

If vec a , vec b , vec c are three non-coplanar vectors, prove that [ vec a+ vec b+ vec c vec a+ vec b vec a+ vec c]=-[ vec a vec b vec c]

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 coplanar vectors, prove that |[vec a, vec b, vec c],[vec a.vec a ,vec a.vec b,vec a.vec c],[vec b.vec a, vec b.vec b, vec b.vec c]|=vec 0 .

If vec a , vec b and vec c are three proper vectors such that vec a * vec b=vec c , vec b*vec c=vec a . Prove that vec a , vec b , vec c are mutually at right angles and |quad vec b|=1 ,|quad vec c|=|quad vec a|.

Let vec a,vec b,vec c are three non-zero vectors such that vec a xxvec b=vec c and vec b xxvec c=vec a; prove that vec a,vec b,vec c are mutually at righ angles such that |vec b|=1 and |vec c|=|vec a|

For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ , vec b+ vec c\ , vec c+ vec a]=2\ [ vec a\ vec b\ vec c]dot

For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ vec b+ vec c\ vec c+ vec a]=2\ [ vec a\ vec b\ vec c]dot

If vec a,vec b, and vec c are three vectors such that vec a xxvec b=vec c,vec b xxvec c=vec a,vec c xxvec a=vec b then prove that |vec a|=|vec b|=|vec c|