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.

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

If vec a , vec b ,a n d vec c are three non-coplanar vectors, then find the value of ( vec a .( vec bxx vec c))/( vec b .( vec cxx vec a))+( vec b .( vec cxx vec a))/( vec c .( vec axx vec b))+( vec c . ( vec bxx vec a))/( vec a . ( vec bxx vec c))

If vec a , vec ba n d vec c are unit coplanar vectors, then the scalar triple product [2 vec a- vec b2 vec b- vec c2 vec c- vec a] is 0 b. 1 c. -sqrt(3) d. sqrt(3)

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 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

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

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

[( 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]

Let vec a , vec b ,a n d vec c be non-coplanar vectors and let the equation vec a^' , vec b^' , vec c ' are reciprocal system of vector vec a , vec b , vec c , then prove that vec axx vec a^'+ vec bxx vec b^'+ vec cxx vec c ' is a null vector.

If vec a , vec b and vec c are three non-zero, non coplanar vector vec b_1= vec b-( vec b . vec a)/(| vec a|^2) vec a , vec c_1= vec c-( vec c . vec a)/(| vec a|^2) vec a+( vec b . vec c)/(| vec c|^2) vec b_1 , , c_2= vec c-( vec c . vec a)/(| vec a|^2) vec a-( vec b . vec c)/(| vec b_1|^2) , b_1, vec c_3= vec c-( vec c . vec a)/(| vec c|^2) vec a+( vec b . vec c)/(| vec c|^2) vec b_1 , vec c_4= vec c-( vec c . vec a)/(| vec c|^2) vec a=( vec b . vec c)/(| vec b|^2) vec b_1 then the set of orthogonal vectors is a. ( vec a , vec b_1, vec c_3) b. ( vec a , vec b_1, vec c_2) c. ( vec a , vec b_1, vec c_1) d. ( vec a , vec b_2, vec c_2)