To get a zero resultant, the vectors must form a closed polygon when added head-to-tail.

• 2 non-zero vectors can give zero only if they are equal and opposite, which are always collinear (same line), not in different planes.

• 3 non-zero vectors can give zero if they form a closed triangle. Three non-collinear vectors always lie in a plane, and they can add up to zero.

Example:

where the three vectors form the sides of a triangle taken in order.
Therefore, the minimum number of non-zero vectors required is 3 .