(i) If three vectors; a, b and c given zero resultant, then vector a + b + c = 0 or a -(vector b + c) i.e vectors a ,b and c will give zero resultant, if vector a is equal to negative of vector (b + c). Because vector (b + c) lies in the plane b and c hence a will be negative of vector (b + c), vector a, b and c all lie in plane.
(ii) Form above discussion, it also follows that three vectors cannot give zero resultant, if they do not lie in a plane.
