In steady flow, pathlines, streamlines, and streaklines are all identical. Let's understand the definitions of these terms and how they relate to each other.

Pathline:
A pathline is the actual path traced by a fluid particle as it moves through a flow field over a period of time. It is the trajectory followed by an individual fluid particle. Pathlines can be visualized as the curve traced by a dye or a marker injected into the fluid at a particular point.

Streamline:
A streamline is an imaginary line that is tangent to the velocity vector at every point in a flow field. It represents the instantaneous direction of fluid flow at each point. Streamlines can be visualized as a set of lines that are parallel to each other and provide a snapshot of the flow field at a specific instant.

Streakline:
A streakline is the locus of all fluid particles that have previously passed through a given point in the flow. It represents the path followed by a continuous line of fluid particles that have been marked at different times. Streaklines can be visualized as lines formed by a continuous injection of dye or tracer particles into the fluid.

Relationship between pathlines, streamlines, and streaklines:
In steady flow, the velocity of fluid particles at a given point remains constant over time. This means that the path traced by a fluid particle (pathline), the direction of flow at each point (streamline), and the line formed by continuously marked fluid particles (streakline) will all be the same.

Explanation of the correct answer:
The correct answer is option 'D' because in steady flow, pathlines, streamlines, and streaklines are all identical. This means that the trajectory followed by an individual fluid particle (pathline), the instantaneous direction of fluid flow at each point (streamline), and the path followed by a continuous line of marked fluid particles (streakline) will all coincide with each other. In other words, they represent the same flow pattern in steady flow conditions.

It is important to note that this relationship between pathlines, streamlines, and streaklines holds true only for steady flow. In unsteady flow, where the velocity at a given point changes over time, pathlines, streamlines, and streaklines will be different from each other.

Overall, understanding the concepts of pathlines, streamlines, and streaklines helps in analyzing and visualizing fluid flow patterns, and their identification is essential in fluid dynamics and engineering applications.