Show that if `vec(a)+vec(b), vec(b)+vec(c ), vec(c )+vec(a)` are coplanar, then `vec(a), vec(b), vec(c )` are also coplanar.

The vectors vec a,vec b,vec c,vec d are coplanar then

If vec(a) + vec(b)+vec(c)=vec(0) , then which of the following is/are correct? 1. vec(a), vec(b), vec(c) are coplanar. 2. vec(a)xx vec(b) = vec(b) xx vec(c) = vec(c) xx vec(a) Select the correct answer using the code given below.

[vec(a)vec(b)vec(c )]=[vec(b)vec(c )vec(a)]=[vec(c )vec(a)vec(b)] .

If vec(a)=vec(b)+vec(c ) , then |vec(a)|=|vec(b)+vec(c )| .

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 the vectors vec a-2vec b+3vec c,vec a-3vec b+5vec c and -2vec a+3vec b-4vec c are coplanar,where vec a,vec b,vec c are non-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.

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

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