In a streamline flow of fluid, the velocity of all fluid particles crossing a given position is constant. This means that the fluid particles moving along a streamline have the same velocity magnitude and direction when they pass through a specific point. However, it is important to note that the velocity of individual fluid particles may vary as they move along the streamline.

Option 1 states that the velocity of all fluid particles at a given instant is constant. This is not accurate because the velocity of individual fluid particles may change as they move along the streamline.

Option 2 states that the speed of a fluid particle remains constant. While the speed of a fluid particle may remain constant if there is no change in its magnitude, it does not imply that the velocity remains constant, which includes both speed and direction.

Option 4 states that the velocity of a fluid particle remains constant. This is also incorrect because, as mentioned earlier, the velocity of individual fluid particles may change along the streamline.

Therefore, option 3 is the correct answer as it correctly describes the behavior of the velocity of all fluid particles crossing a given position in a streamline flow.