If `a ,ba n dc` are non-cop0lanar vector, then that prove `|( vec adot vec d)( vec bxx vec c)+( vec bdot vec d)( vec cxx vec a)+( vecc dot vec d)( vec axx vec b)|` is independent of `d ,w h e r ee` is a unit vector.

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

[vec a, vec b + vec c, vec d] = [vec a, vec b, vec d] + [vec a, vec c, vec d]

For any four vectors,prove that (vec b xxvec c)*(vec a xxvec d)+(vec c xxvec a)*(vec b xxvec d)+(vec a xxvec b)*(vec c xxvec d)=0

If vec a,vec c,vec d are non-coplanar vectors,then vec d*{vec a xx[vec b xx(vec c xxvec d)]} is equal to

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot

The vector component of vec b perpendicular to vec a is ( vec bdot vec c) vec a b. ( vec axx( vec bxx vec a))/(| vec a|^2) c. vec axx( vec bxx vec a) d. none of these

For any three vectors adotb\ a n d\ c write the value of vec axx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)dot

Prove that [vec a,vec b,vec c+vec d]=[vec a,vec b,vec c]+[vec a,vec b,vec d]

vec axx( vec bxx vec c) , vec bxx( vec cxx vec a) and vec cxx( vec axx vec b) are: linearly dependent (b) coplanar vector parallel vectors (d) non coplanar vectors

If vec a, vec b, vec c are three non-coplanar vectors such that vec a + vec b + vec c = alphavec d and vec b + vec c + vec d = betavec a then vec a + vec b + vec c + vec d is equal to