If the vectors `vec(a) + vec(b), vec(b) + vec(c)` and `vec(c) + vec(a)` are coplanar, then prove that the vectors `vec(a), vec(b)` and `vec(c)` are also coplanar.

Show that the vectors vec a - vec b, vec b - vec c , vec c - vec a are coplaner.

If vec(a)vec(b)vec(c ) and vec(d) are vectors such that vec(a) xx vec(b) = vec(c ) xx vec(d) and vec(a) xx vec(c ) = vec(b)xxvec(d) . Then show that the vectors vec(a) -vec(d) and vec(b) -vec(c ) are parallel.

Show that vec(a), vec(b), vec(c ) are coplanar if and only if vec(a) + vec(b), vec(b) + vec(c ), vec( c) + vec(a) are coplanar

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)

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)

Show that the vectors vec a-2 vec b+3 vec c , vec a-3 vec b+5 vec ca n d-2 vec a+3 vec b-4 vec c are coplanar, where vec a , vec b , vec c are non-coplanar.

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) times vec(b)=vec(c) and vec(b) times vec(c)=vec(a)," prove that "vec(a), vec(b), vec(c) are mutually perpendicular and abs(vec(b))=1 and abs(vec(c))=abs(vec(a)) .

If vec(a), vec(b), vec(c ) are three vectors such that vec(a) + vec(b) + vec(c ) = 0 and | vec(a) | =2, |vec(b) | =3, | vec(c ) = 5 , then the value of vec(a). vec(b) + vec(b) . vec( c ) + vec(c ).vec(a) is

Show that the vectors vec a , vec b and vec c are coplanar if vec a+ vec b , vec b+ vec c and vec c+ vec a are coplanar.

If vec(A) , vec(B) and vec(C ) are three vectors when you can say that vec(A) + vec(B) = vec(C ) and A+B = C are the same ?