Consider four planes with the Cartesian equations:

- Establish that two of them are parallel and the other two are perpendicular.
- For the two parallel planes, find the distance between them.

- The second and fourth planes are parallel since they have the same normal vector, .

To see that the first and third are perpendicular, we denote the normal vectors by and , respectively, and compute

Hence, they are perpendicular.

- Denoting the second and fourth planes by and , respectively we have Cartesian equations

Therefore, the distance between them is

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