Distance between two parallel planes

[kahwawashay1]

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

 

[micromass]

Do you know how to find the distance between a point and a plane??

 

[HallsofIvy]

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.

 

[Tarantinism]

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)