Final answer:
The correct answer to the vector displacement problem is that the plane changed direction and traveled a longer distance than 300 km, as option (d) correctly states.
Step-by-step explanation:
The student's question pertains to vector displacement and total distance traveled by a plane. In scenario (a), a plane travels 300 km South and then 200 km South 31ยบ East. If we were to analyze this using vector addition, the total distance traveled would indeed be 500 km when simply adding the magnitudes of the two distances. However, option (b) is incorrect because the plane did not travel 100 km in a straight line, and neither did it travel 300 km in a straight line as mentioned in option (c). The correct answer is (d), where the plane changed direction and traveled a longer distance than 300 km, as the resultant vector combining both displacement vectors will be greater than 300 km but less than 500 km due to the Pythagorean theorem applied to the combined vector components.