Final answer:
Two vectors with equal magnitudes and opposite directions will sum to zero, resulting in a resultant vector with a magnitude of zero. Vectors of different magnitudes can only sum to zero if three or more vectors are involved and they form a closed shape.
Step-by-step explanation:
If two vectors have equal magnitudes and are opposite in direction, their sum can indeed be zero. This is because vectors are not just numbers; they have both magnitude and direction. When two vectors of the same magnitude point in exactly opposite directions, they cancel each other out. Their resultant vector's magnitude is zero, meaning there is no net vector.
For example, consider two force vectors, each with a magnitude of 20 Newtons, but one points upward and the other points downward. Algebraically, if the upward force is represented as +20 N and the downward force as -20 N, their sum is 0 N, which aligns with vector addition principles. In the case of steps, if two steps are of equal length but in opposite directions, then you will end up at your starting point. However, for vectors of different magnitudes, the only way their sum can be zero is if more than two vectors are involved, and they form a closed polygon when placed tip-to-tail, effectively canceling each other out.