If the three vectors ` vec a+ vec b , vec b+ vec c` and ` vec c+ vec a` are also coplanar.

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

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 , vec c are three non-zero vectors (no two of which are collinear), such that the pairs of vectors (vec a + vec b, vec c) and (vec b + vec c , vec a) are collinear, then vec a + vec b + vec c =

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 vectors vec a ,\ vec b ,\ vec c are coplanar 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)

If vec a ,\ vec b ,\ vec c are three vectors such that vec a. vec b= vec a.\ vec c and vec a\ xx\ vec b= vec a\ xx\ vec c ,\ vec a\ !=0 , then show that vec b= vec c .

Let vec a , vec ba n d vec c , be non-zero non-coplanar vectors. Prove that: vec a-2 vec b+3 vec c ,-2 vec a+3 vec b-4 vec ca n d vec c-3 vec b+5 vec c are coplanar 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.

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.