Distance between parallel planes
The distance between parallel planes is equal to the value of the perpendicular drawn from a point belonging to one plane to another plane. The distances between two parallel planes can be determined using the coordinate method.
.Distance between parallel planes
Examples of tasks for calculating the distance between planes
Example #1: Find the distance between the planes 4x + 8y – 8z – 12 = 0 и 2x + 4y – 4z + 18 = 0.
At the beginning, it is necessary to check whether the planes are equal, for this it is necessary to multiply the equation of the second plane by the equation of the second plane on 2: 4x + 8y – 8z + 36 = 0. Now we enter the necessary data into the calculator.
Ответ: the distance between the planes is equal to 4.
Example #2: Find the distance between the planes 3x + 5y – 7z – 12 = 0 и 1.5x + 2.5y – 3.5z + 9 = 0.
At the beginning, it is necessary to check whether the planes are equal, for this it is necessary to multiply the equation of the second plane by 2: 3x + 5y – 7z + 18 = 0. Now we enter the necessary data into the calculator.
Answer: the distance between the planes is equal to 3.29