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]`

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

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|

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|

Prove that,for any three vectors vec a,vec b,vec c[vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

If vec a , vec b and vec c are three non-zero, non coplanar vector vec b_1= vec b-( vec bdot vec a)/(| vec a|^2) vec a , vec c_1= vec c-( vec cdot vec a)/(| vec a|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , , c_2= vec c-( vec cdot vec a)/(| vec a|^2) vec a-( vec bdot vec c)/(| vec b_1|^2) , b_1, vec c_3= vec c-( vec cdot vec a)/(| vec c|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , vec c_4= vec c-( vec cdot vec a)/(| vec c|^2) vec a=( vec bdot vec c)/(| vec b|^2) vec b_1 then the set of orthogonal vectors is ( vec a , vec b_1, vec c_3) b. ( vec a , vec b_1, vec c_2) c. ( vec a , vec b_1, vec c_1) d. ( vec a , vec b_2, vec c_2)

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 and vec c be any three vectors then show that vec a+(vec b+vec c)=(vec a+vec b)+vec c

Let vec a,vec b and vec c, be non-zero non-coplanar vectors. Prove that: vec a-2vec b+3vec c,-2vec a+3vec b-4vec c and vec c-3vec b+5vec c are coplanar vectors. 2vec a-vec b+3vec c,vec a+vec b-2vec c and vec a+vec b-3vec c are non-coplanar vectors.

Let vec a, vec b, vec c be three non-zero vectors such that [vec with bvec c] = | vec a || vec b || vec c | then

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))