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Distance between a parallel line and plane

Line r passes through A(25, 8, 9) and is parallel to plane α with normal (2, 1, 2) through B(20, 10, 4). Find the distance between r and α.

Step-by-step solution

1. Since the line is parallel to the plane, every point of it is at the same distance.
2. Take any point of the line, for example A.
3. Measure the distance from A to the plane: perpendicular through A, foot I and segment AI.
4. Check that AI is perpendicular to the plane.

Result: I(21, 6, 5); distance = 6 units.

Do not measure from a point that just “looks right”; any point of the line works because it is parallel.

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