Can you provide some example problems involving Miller indices?

Here are some example problems involving Miller indices:

1. Determine the Miller indices for a plane that intersects the x-axis at (1,0,0), the y-axis at (0,1,0), and the z-axis at (0,0,1).

2. Calculate the Miller indices for a plane that passes through the points (2,1,0), (0,3,1), and (-1,0,4).

3. Find the Miller indices for a plane that intersects the x-axis at (1,0,0), the y-axis at (-1,1,0), and the z-axis at (0,0,2).