Is the distance shorter between Atlanta and Miami or between Atlanta or Indianapolis?
Atlanta to Indy is shorter than Atlanta to Miami.
If you notice that the number of waves that go past increases you also find that the distance between each crest?
Africa is a massive continent. It's northern part is close to Europe, where Austria is, so it would be closer to Austria. There are parts of Africa that would be closer to South America than to Austria, but the shortest distance between Austria and Africa would be much shorter than the shortest distance between Africa and South America.
The shortest distance between any two points, A and B, in a plane is the straight line joining them. Suppose, that the distance A to C and then C to B is shorter where C is any point not on AB. That would imply that, in triangle ABC, the sum of the lengths of two sides (AC and CB) is shorter tan the third side (AB). That contradicts the inequality conjecture.
You may be thinking of the distance between lines of longitude. The length of the lines of latitude decrease because the Earth is round, so the length of the line is shorter at the poles than it is at the Equator. The distance between the lines of longitude is shorter as you move toward the poles, again, because the Earth is round. All lines of longitude are the same length.
How does the distance moved by an object between its starting point and its ending point compare with the displacement vector between the same point?
Distance is 11,012 kilometers or 6,843 miles or 5,946 nautical miles The distance is the theoretical air distance (great circle distance). Flying between the two locations's airports can be longer or shorter, depending on airport location and actual route chosen Straight line distance is 10,999 kilometers or 6,834 miles.
If you define 'distance' as the shortest line between to objects. (Example: the moon and the Earth; or say, Suburb A and Suburb B, then such distances are measured in Metre if the distance is shorter than around about 1 Kilometre, or,. If the distance is greater than a few hundred Metre, it is always measured in Kilometre.