Final answer:
When two vectors a and b with magnitudes a and b respectively, and a > b, are added, the magnitude of the resultant vector will always be greater than b. The precise magnitude will range between a + b and |a - b| depending on the vectors' relative directions.
Step-by-step explanation:
When adding two vectors a and b with magnitudes a and b respectively, where a > b, several outcomes for the magnitude of the resultant vector are possible depending on the direction of the vectors. If vectors aƒ— and bƒ— are added together in the same direction (they are parallel), then the magnitude of the resultant vector will be the sum of the magnitudes, which means R = a + b. In this case, the magnitude of the resultant vector is greater than both a and b, which follows option 3. If vectors aƒ— and bƒ— are in exactly opposite directions (antiparallel), the magnitude of the resultant vector would be the absolute difference of their magnitudes, therefore R = |a - b|. The magnitude of the resultant vector would then be less than a but still greater than b. However, if the vectors are at any other angle, the magnitude of the resultant vector would be somewhere between a + b and |a - b|, but it will always be greater than b. Therefore, the magnitude of the resultant vector will never be equal to a or b specifically, but it could fall within the range mentioned especially for option 4.