Streamline:
A streamline is a line that is tangent to the velocity vector at every point in a fluid flow field. It represents the instantaneous direction of flow at any given point. Streamlines are used to visualize the flow pattern and identify the direction of fluid motion.

Pathline:
A pathline is the actual trajectory of a fluid particle as it moves through the flow field over a given period of time. It represents the complete path followed by a fluid particle from its initial position to its final position. Pathlines provide information about the history of fluid motion and can be used to track the movement of specific particles.

Streakline:
A streakline is the locus of particles that have previously passed through a specific point in the flow field. It represents the path followed by all the fluid particles that have passed through a given position at a specific instant in time. Streaklines provide information about the time evolution of fluid motion and can be used to study the mixing and dispersion of particles.

Geometrical Distinction:
In the case of steady flow, there is no change in the flow pattern with time. The velocity field remains constant over time, and therefore the streamlines, pathlines, and streaklines coincide with each other. This means that the geometrical distinction between the three types of lines is lost in steady flow.

Explanation:
Steady flow refers to a flow field where the velocity of the fluid does not change with time. In such a flow, the streamlines, pathlines, and streaklines are the same because the fluid particles follow the same paths over time.

In the case of steady flow, the streamlines depict the instantaneous direction of flow at any given point. Since the flow field does not change with time, the path followed by a fluid particle (pathline) and the locus of particles that have passed through a specific point (streakline) are the same as the streamline at any given instant.

Thus, in steady flow, there is no geometrical distinction between the streamline, pathline, and streakline. They represent the same line in the flow field. This is because the flow pattern remains constant over time, and the particles follow the same paths regardless of the time duration.

On the other hand, in unsteady flow, such as in the case of time-varying velocity fields or fluid motion with changing patterns, the streamlines, pathlines, and streaklines are different from each other, and they provide distinct information about the flow behavior.

Therefore, in the given options (a) steady flow, there is no geometrical distinction between the streamline, pathline, and streakline.