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.

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

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

For any three vectors vec(a), vec(b) and vec(c) , show that vec(a) - vec(b), vec(b) - vec(c) , vec(c) - vec(a) are coplanar.

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

For any three coplanar vectors vec(a), vec(b), vec(c ) , show that vec(a)-vec(b), vec(b)-vec(c ), vec(c )-vec(a) are 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 vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec a are coplanar.