Question

you go on vacation and have the map above. what kind of values are given by the map? vector quantities scalar quantities neither

Explanation:

To determine the type of values, we recall:

• Scalar quantities have magnitude (size) only (e.g., distance, speed, mass).
• Vector quantities have magnitude and direction (e.g., displacement, velocity, force).

The map shows distances (125 km, 65 km, etc.) with directional arrows (implied by the path’s turns and the compass). However, the values (the numbers with “km”) represent magnitude (distance) without explicitly labeling direction as part of the value itself. Wait—no, actually, the path includes direction (via the arrows), but the quantities given (the distances) are scalars because distance is a scalar (displacement would be a vector, but here we have distance values). Wait, no—wait: the map’s values (e.g., 125 km, 65 km) are magnitudes of distance, which is a scalar. But the path has direction (implied by the arrows), but the values (the numbers with units) are scalars because they only have magnitude, not direction as part of the value. Wait, no—actually, the arrows indicate direction, but the values (like 125 km) are scalar quantities (distance) because they lack direction in their numerical representation (direction is shown by the path’s orientation, not the value itself). Wait, no—maybe I confused. Let’s re-express:

• Scalar: magnitude only (e.g., 5 km, 10 m/s speed).
• Vector: magnitude + direction (e.g., 5 km north, 10 m/s east).

The map’s values (125 km, 65 km, etc.) are magnitudes of distance (a scalar), and the direction is shown by the path’s arrows (not part of the value). So the values given (the numbers with km) are scalar quantities because they only represent magnitude (distance), not direction as part of the value. Wait, but the path has direction—does that make the values vectors? No, because the value (e.g., 125 km) is just magnitude; the direction is from the path’s orientation, not the value itself. So the values (the numerical distances) are scalars.

Answer:

B. scalar quantities