Answer :
Final answer:
The line along the shortest distance between two lines L1 and L2 is the line that is perpendicular to both. This is because a perpendicular line ensures the minimum distance between the points of the lines it intersects. The theorem of parallel axes also reflects this principle by considering the perpendicular distance in rotational physics.
Explanation:
The question concerns the shortest line that can be drawn with respect to two given lines, L1 and L2. This is a concept in geometry concerning the relationship between lines and distances in a plane or three-dimensional space.
If we are looking for the line that connects the two given lines with the shortest distance, then the correct answer is a line that is perpendicular to both L1 and L2. This ensures that the shortest possible distance is achieved. Parallel lines maintain a constant distance, and bisecting an angle or the perpendicular distance does not assure the shortest path between two lines unless they are parallel, which is not specified in the question.
Euclidean geometry tells us that only a perpendicular line will ensure this minimum distance is maintained. According to the theorem of parallel axes, in the context of rotational physics, the distance considered here as d is the perpendicular distance between two parallel axes. This is analogous to the situation in geometry where the shortest distance between two lines is along the perpendicular.
To apply this concept to two non-parallel lines, consider the place where their perpendicular bisectors would intersect; this point would be equidistant from the two lines, and it's this perpendicular line that will actually connect them at their closest points. Therefore, the line along the shortest distance is constituted by the line that is perpendicular to L1 and L2.
