Final answer:
Two vectors of unequal magnitude cannot sum to zero; they must be equal in magnitude and opposite in direction to do so. However, three or more vectors can sum to zero even if their magnitudes are not equal, as long as they form a closed shape.
Step-by-step explanation:
The question asks if two vectors of unequal magnitude can sum to zero. The answer is No. For two vectors to sum to zero, they must be equal in magnitude and opposite in direction. Imagine walking in one direction and then taking a step of the exact same length but in the opposite direction – you would end up where you started, which means the two displacement vectors sum to zero.
However, when three or more vectors are involved, it is possible for them to sum to zero even if they do not all have the same magnitude. They just need to be arranged in such a way that they form a closed shape, like a triangle or a rectangle.
To address one of the example questions, when two vectors are equal in magnitude and opposite in direction, their resultant vector has a magnitude of zero because they cancel each other out. Also, the average velocity can indeed be negative if the net displacement is in the opposite direction of the defined positive direction. Lastly, we can use the Pythagorean theorem to calculate the magnitude of the resultant vector when two vectors are at right angles to each other.