If `( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c` are nonzero vectors, then 1.` vec a , vec b ,a n d vec c` can be coplanar 2.` vec a , vec b ,a n d vec c` must be coplanar 3.` vec a , vec b ,a n d vec c` cannot be coplanar 4.none of these

If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot

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 r . vec a= vec r . vec b= vec r . vec c=0,w h e r e vec a , vec b ,and vec c are non-coplanar, then a. vec r_|_( vec cxx vec a) b. vec r_|_( vec axx vec b) c. vec r_|_( vec bxx vec c) d. vec r= vec0

Given that vec adot vec b= vec adot vec c , vec axx vec b= vec axx vec c and vec a is not a zero vector. Show that vec b= vec c dot

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

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

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) a. [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= a. [ vec a\ vec b\ vec c] b. 0 c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

If vec axx vec b= vec cxxvec d and vec axxvec c= vec bxxvec d, vec a ne vec d, vec b ne vec c then show that vec b- vec c is parallel to vec a-vec d

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| .