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 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 ba n d vec c are non-coplanar vectors, prove that the four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec c ,3 vec a+ 4 vec b-2 vec ca n d vec a-6 vec b+6 vec c are coplanar.

[( 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]

Show that | vec a| vec b+| vec b| vec a is a perpendicular to | vec a| vec b-| vec b| vec a , for any two non-zero vectors vec aa n d vec bdot

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

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

Given three non-zero, non-coplanar vectors vec a , vec b ,and vecc .vec r_1=p vec a+q vec b+ vec ca n d vec r_2= vec a+p vec b+q vecc dot If the vectors vec r_1+2 vec r_2 and 2 vec r_1+ vec r_2 are collinear, then (p ,q) is

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

( 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]

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