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). (vec b- vec c)!=0,`

If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , then show that vec a- vec d , is paralelto vec b- vec c

If veca , vec b , vec c are three vectors such that veca+ vec b+ vec c= vec0 , then prove that vec axx vec b= vec bxx vec c= vec cxx vec a

If vec a , vec b , and 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| .

If vec aa n d 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]dot

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

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then

36. If vec a, vec b,vec c and vec d are unit vectors such that (vec a xx vec b) . vec c xx vec d= 1 and vec a.vec c =1/2 then a) vec a, vec b and vec c are non-coplanar b) vec b, vec c ,vec d are non -coplanar c) vec b, vecd are non parallel d) vec a , vec d are parallel and vec b, vec c are parallel

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 , vec ca n d vec d are the position vectors of the vertices of a cyclic quadrilateral A B C D , prove that (| vec axx vec b+ vec bxx vec d+ vec d xx vec a|)/(( vec b- vec a)dot( vec d- vec a))+(| vec bxx vec c+ vec cxx vec d+ vec d xx vec b|)/(( vec b- vec c)dot( vec d- vec c))=0dot

If vec a ,\ vec b ,\ vec c are three unit vecrtors such that vec axx vec b= vec c ,\ vec bxx vec c= vec a ,\ vec cxx vec a= vec b Show that vec a ,\ vec b ,\ vec c form an orthonormal right handed triad of unit vectors.