If ` vec a , vec b , vec ca n d vec d` are distinct vectors such that ` vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d ,` prove that `( vec a- vec d)dot (vec b- vec c)!=0,`

If vec a , vec b ,a n d vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c|dot

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].

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 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| .

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

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 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

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

If vec a , vec b , vec c are any three noncoplanar vector, then the equaltion [ vec bxx vec c vec cxx vec a vec axx vec b]x^2+[ vec a+ vec b vec b+ vec c vec c+ vec a]x+1+[ vec b- vec c vec c- vec a vec a- vec b]=0 has roots a. real and distinct b. real c. equal d. imaginary