For two vectors `vec(A)` and `vec(B)` if `vec(A) + vec(B) = vec(C)` and `A +B = C`, then prove that `vec(A)` and `vec(B)` are parallel to each other.

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.

Three vector vec(A) , vec(B) , vec(C ) satisfy the relation vec(A)*vec(B)=0 and vec(A).vec(C )=0 . The vector vec(A) is parallel to

Three vector vec(A) , vec(B) , vec(C ) satisfy the relation vec(A)*vec(B)=0 and vec(A).vec(C )=0 . The vector vec(A) is parallel to

Three vector vec(A) , vec(B) , vec(C ) satisfy the relation vec(A)*vec(B)=0 and vec(A).vec(C )=0 . The vector vec(A) is parallel to

Three vector vec(A) , vec(B) , vec(C ) satisfy the relation vec(A)*vec(B)=0 and vec(A).vec(C )=0 . The vector vec(A) is parallel to

Three vector vec(A) , vec(B) , vec(C ) satisfy the relation vec(A)*vec(B)=0 and vec(A).vec(C )=0 . The vector vec(A) is parallel to

If vec(a) xx vec(b) = vec(c ) xx vec(d) and vec(a) xx vec(c )= vec(b) xx vec(d) then show that vec(a)- vec(d) and vec(b) -vec(c ) are parallel vectors.

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) + vec(b) + vec(c) = vec(0) , then prove that vec(a) xx vec(b) = vec(b) xx vec(c) = vec(c) xx vec(a) .

Three non-zero vectors vec(a), vec(b), vec(c) are such that no two of them are collinear. If the vector (vec(a)+vec(b)) is collinear with the vector vec(c) and the vector (vec(b)+vec(c)) is collinear with vector vec(a) , then prove that (vec(a)+vec(b)+vec(c)) is a null vector.