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Distance between two parallel planes

Find the distance between the parallel planes α and β given by their normals and constant terms.

Step-by-step solution

1. Take any point P on α.
2. Draw through P the perpendicular to the planes (normal direction).
3. Find Q, where that perpendicular cuts β.
4. Segment PQ is the distance; check that it is perpendicular to both planes.

Result: P(2.27, 5.09, 6.09), Q(0.36, 4.45, 5.45); distance = 2.11 units.

The distance is measured along the common perpendicular, not along a slanted line joining the planes.

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