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`

Let vec a , vec b ,and 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]^2

Let vec a , vec b ,and 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]^2

For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ vec b+ vec c\ vec c+ vec a]=2\ [ vec a\ vec b\ vec c]dot

For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ , vec b+ vec c\ , vec c+ vec a]=2\ [ vec a\ vec b\ vec c]dot

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .

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 , 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

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 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)