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 vec b is not perpendicular to vec c , then find the vector vec r satisfying the equation vec rxx vec b= vec axx vec b and vec r. vec c=0.

If vector vec x satisfying vec x xx vec a+( vec x . vec b) vec c= vec d is given vec x=lambda vec a+ vec axx( vec axx( vec d xx vec c))/(( vec a . vec c)| vec a|^2) , then find the value of lambdadot

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 , 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 vec a , vec b , vec c are mutually perpendicular unit vectors, find |2 vec a+ vec b+ vec c|dot

If | vec a|+| vec b|=| vec c| and vec a+ vec b= vec c , then find the angle between vec a and vec bdot

If vec a , vec ba n d vec c are unit vectors satisfying | vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2=9, then |2 vec a+5 vec b+5 vec c| is.

Given vec(C )= vec(A) xx vec(B) and vec(D) = vec(B) xx vec(A) . What is the angle between vec(C ) and vec(D) ?

Given | vec a|=| vec b|=1a n d| vec a+ vec b|=sqrt(3). If vec c is a vector such that vec c- vec a-2 vec b=3( vec axx vec b), then find the value of vec c. vec b

If vectors vec aa n d vec b are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to a is a. vec b+( vec bxx vec a)/(| vec a|^2) b. ( vec adot vec b)/(| vec b|^2) c. vec b-( vec bdot vec a)/(| vec a|^2) d. ( vec axx( vec bxx vec a))/(| vec b|^2)