A,B,C,D are four points in the space and satisfy `| vec A B|=3,| vec B C|=7,| vec C D|=11&| vec D A|=9` , then value of ` vec (AC). vec(BD)` .

A, B, C, D are four points in the space and satisfy |vec(AB)|=3, |vec(BC)|=7, |vec(CD)|=11 and |vec(DA)|=9 . Then find the value of vec(AC)*vec(BD) .

A , B , Ca n dD are any four points in the space, then prove that | vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4 (area of A B C .)

A , B , Ca n dD are any four points in the space, then prove that | vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4 (area of A B C .)

A , B , Ca n dD are any four points in the space, then prove that | vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4 (area of A B C .)

If A ,B ,C ,D be any four points in space, prove that | vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4 (Area of triangle ABC)

A , B , C , D are any four points, prove that vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=0.

A , B , C , D are any four points, prove that vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=4(Area \ of triangle ABC).

If A ,B ,C ,D are four distinct point in space such that vec(A B) is not perpendicular to vec(C D) and satisfies vec (A B).vec (C D)=k(| vec(A D)|^2+| vec(B C)|^2-| vec(A C)|^2-| vec(B D)|^2), then find the value of kdot

If A ,B ,C ,D are four distinct point in space such that A B is not perpendicular to C D and satisfies vec A Bdot vec C D=k(| vec A D|^2+| vec B C|^2-| vec A C|^2=| vec B D|^2), then find the value of kdot

Given three vectors vec a , vec b ,a n d vec c two of which are non-collinear. Further if ( vec a+ vec b) is collinear with vec c ,( vec b+ vec c) is collinear with vec a ,| vec a|=| vec b|=| vec c|=sqrt(2)dot Find the value of vec a. vec b+ vec b. vec c+ vec c. vec a a. 3 b. -3 c. 0 d. cannot be evaluated