Final answer:
The magnitude of the sum of two displacement vectors of 5 m and 7 m depends on the angle between them. Options 2 m, 12 m, and 8 m could all be correct under different circumstances.
Step-by-step explanation:
When two displacement vectors are added, the magnitude of the sum can vary depending on the direction of the vectors in relation to each other. If the vectors are in the exact same or opposite directions, their magnitudes can be directly added or subtracted. However, if the vectors are not aligned, one must use vector addition rules, such as the Pythagorean theorem for perpendicular vectors, or the law of cosines for vectors at other angles, to find the magnitude of the resultant vector.
In the case where two displacement vectors have magnitudes of 5 m and 7 m respectively, the possible magnitude of the sum is not given by simple addition or subtraction. The minimum magnitude, when the vectors are in opposite directions, would be 2 m (not considering the vector direction), and the maximum magnitude, when the vectors are in the same direction, would be 12 m. The resultant magnitude of 8 m would be the case if the vectors are perpendicular to each other. Without additional information on the directions of the vectors, the exact magnitude of the sum cannot be determined. Therefore, any of the choices A. 2 m, B. 12 m, and D. 8 m could be potentially correct depending on the directions of the vectors.