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.

For any four vectors, prove that ( vec bxx vec c)dot( vec axx vec d)+( vec cxx vec a)dot( vec bxx vec d)+( vec axx vec b)dot( vec cxx vec d)=0.

If vec u , vec va n d vec w are three non-cop0lanar vectors, then prove that ( vec u+ vec v- vec w)dot( vec u- vec v)xx( vec v- vec w)= vec udot vec vdotxx vec w

If vectors b ,ca n dd are not coplanar, then prove that vector ( vec axx vec b)xx( vec cxx vec d)+( vec axx vec c)xx( vec d xx vec b)+( vec axx vec d)xx( vec bxx vec c) is parallel to vec adot

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

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)

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

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

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|=0

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0