Distance between two parallel planes

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    Parallel Planes
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Discussion Overview

The discussion centers on the method for calculating the distance between two parallel planes, including the derivation of the formula used for this calculation. Participants explore different approaches and reasoning related to this geometric concept.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant asks for clarification on how to find the distance between two parallel planes, noting that their textbook only provides a formula without derivation.
  • Another participant inquires about finding the distance between a point and a plane, suggesting a related concept.
  • A different approach is proposed, where one can choose a point on one plane, write the equation for a line perpendicular to that plane, and find where it intersects the second plane to calculate the distance.
  • Another participant suggests that when the planes are parallel, the distance can be determined using a common unit normal vector and the scalar product of a vector joining points from both planes with that normal vector, referencing its appearance in educational materials and solid state physics.

Areas of Agreement / Disagreement

Participants present multiple approaches to the problem, indicating that there is no consensus on a single method for deriving the distance between parallel planes.

Contextual Notes

Some assumptions about the planes being parallel and the definitions of the normal vector are implicit in the discussion. The derivation of the formula remains unexplored in detail.

kahwawashay1
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How do you find the distance between two parallel planes? My book gives me only a formula and doesn't say how they got it
 
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Do you know how to find the distance between a point and a plane??
 
Choose any point on one plane. Write the equation for the line perpendicular to given plane through that point. Find the point where that line intersects the second plane. Calculate the distance between the original point and this point on the second plane.
 
Is usually easier:

1. The distance is 0 if the planes are not parallel.

2. When they are parallel, they have a common unit normal vector. Take any vector joining any point of the first plane with any point of the second plane and the scalar product with that normal vector.

This gives the formula which is usually seen in the school-books or in the basic theory of crystal lattices in solid state physics (which gives sort of that "evaluation" of a point at the other plane's equation and dividing by the modulus of the normal vector)
 

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