A resultant vector is zero only when three vectors form a closed shape, such as a triangle, in the first quadrant of an x-y coordinate system. However, if the vectors are represented correctly with their tails at the origin, their sum cannot be zero since adding three positive numbers cannot yield a negative result. Misrepresentation of vectors can lead to confusion, suggesting that a zero resultant is possible when it is not. The discussion emphasizes the importance of accurate vector representation in understanding their resultant. Therefore, in a proper vector setup, three vectors in the first quadrant cannot sum to zero.