Final answer:
The magnitude of the resultant vector from combining two vectors with magnitudes 30m and 90m must be between 60m and 120m. Therefore, 20m cannot be the magnitude of the resultant vector.
Step-by-step explanation:
When dealing with the magnitudes of resultant vectors, the result depends on both the magnitudes of the original vectors and the angle between them. In this scenario, we have two vectors with magnitudes 30m and 90m. The key principle here is that the magnitude of the resultant vector must be between the sum and the difference of the magnitudes of the two vectors when they are aligned in the most and least additive configurations respectively. So, the smallest possible resultant is 60m (90m - 30m), and the largest possible resultant is 120m (90m + 30m).
Given these conditions, option (a) 20m cannot possibly be the magnitude of the resultant of the two vectors because it is less than the smallest possible magnitude of 60m. Options (b) 60m, (c) 80m, and (d) 120m are all within the possible range for the magnitude of a resultant vector formed by combining vectors of 30m and 90m.