Final answer:
The shortest path from the origin to the end of the last vector after vector addition is the resultant vector, which shows the total displacement and is a vector quantity because it has both magnitude and direction. (option b is the correct answer)
Step-by-step explanation:
When adding vectors, the shortest path from the origin to the end of the last vector is called the resultant vector. In vector addition, arrows represent vectors and they are added using the head-to-tail method. This involves drawing the first vector and then connecting the next vector starting at the head of the first vector.
After all vectors are added in this way, the resultant vector is drawn from the tail of the first vector to the head of the last vector. This resultant vector represents the total displacement, which is the direct straight-line distance from the starting point to the final position, and it accounts for the magnitude and direction of the combined vector quantities.
Referring to the specific information given, if a person first walks nine blocks east and then five blocks north, their total displacement does not match the paths they took, but simply connects their starting point with their ending point. Displacement is indeed a vector quantity because it has both magnitude and direction, such as described with a magnitude of 6 km and directed from the starting point to the destination.