If ` vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3` are two sets of vectors such that ` vec e_idot vec E_j=1,ifi=ja n d vec e_idot vec E_j=0a n difi!=j ,` then prove that `[ vec e_1 vec e_2 vec e_3][ vec E_1 vec E_2 vec E_3]=1.`

If vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3 are two sets of vectors such that vec e_idot vec E_j=1,ifi=j and vec e_idot vec E_j=0a n difi!=j , then prove that [ (vec e_1, vec e_2 ,vec e_3)][ (vec E_1, vec E_2, vec E_3) ]=1.

If vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3 are two sets of vectors such that vec e_idot vec E_j=1,ifi=j and vec e_idot vec E_j=0a n difi!=j , then prove that [ (vec e_1, vec e_2 ,vec e_3)][ (vec E_1, vec E_2, vec E_3) ]=1.

If vec e_(1),vec e_(2),vec e_(3) and vec E_(1),vec E_(2),vec E_(3) are two sets of vectors such that vec e_(i)*vec E_(j)=1, if i=j and vec e_(i)*vec E_(j)=0 and if i!=j then prove that [vec e_(1)vec e_(2)vec e_(3)][vec E_(1)vec E_(2)vec E_(3)]=1

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0

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.

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.

A B C D E is pentagon, prove that vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

prove that | vec axx vec b|=( vec adot vec b)t a ntheta, w h e r e theta is the angle between vec a a n d vec bdot

If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot

If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot