Yes, on a sphere, distances can vary depending on the direction or path taken between two points. This is because a sphere has curvature, unlike a flat surface.
To understand this concept, consider the analogy of the Earth's surface. When you travel between two cities on Earth, the distance you cover depends on the path you take, which could be a straight line or a curved route. For example, the distance between two cities measured along the equator would be different from the distance measured along a great circle route (the shortest path on a sphere). Similarly, traveling along different lines of longitude or latitude will result in varying distances.
On a sphere, the shortest distance between two points is known as the great circle distance. It corresponds to the length of the arc along the great circle (the largest circle that can be drawn on the sphere and passes through the two points). Any other path connecting the two points will be longer.
In summary, due to the curvature of a sphere, distances can vary depending on the direction or path taken between two points. The concept of great circle distance is commonly used to determine the shortest path between two points on a sphere.