Understanding the Concept:
For a set of vectors to yield a net zero resultant vector ($\sum \vec{V} = \vec{0}$), they must be able to form a closed polygon loop when joined head-to-tail.
To balance out two vectors, they must be perfectly equal in magnitude and point in opposite directions.
To balance out three vectors, any two vectors must combine into a single resultant that is equal and opposite to the third vector.
Step 1: Evaluate Statement (A).
If three vectors do not lie in the same plane (non-coplanar), two of them will form a plane, and their combined resultant will also lie in that same plane. Because the third vector points outside this plane, it can never cancel out that component. Thus, their resultant can never be zero. Hence, statement (A) is false.
Step 2: Evaluate Statement (B).
If three vectors lie within the same plane (coplanar), they can easily be arranged to form the three closed sides of a triangle loop (e.g., three forces in equilibrium). In this configuration, their vector sum is exactly zero. Hence, statement (B) is true.
Step 3: Evaluate Statement (C).
Two vectors can only form a net zero resultant if they completely cancel each other out. This requires them to point in opposite directions and have identical magnitudes. If their magnitudes differ, a net non-zero leftover force remains. Hence, statement (C) is false.