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Distance between two planes

Distance between two planes
Definition. The distance between two planes is equal to length of the perpendicular lowered from a point on a plane.

Distance between two planes formula

If Ax + By + Cz + D1 = 0 and Ax + By + Cz + D2 = 0 is a plane equation, then distance between planes can be found using the following formula

d |D2 - D1|
A2 + B2 + C2

Examples of tasks with distance between two planes

Example 1.
To find distance between planes 2x + 4y - 4z - 6 = 0 and x + 2y - 2z + 9 = 0.

Solution. Let's check up, whether planes are parallel, for this purpose we will multiply the equation of the second plane on 2

2x + 4y - 4z + 18 = 0

As planes are parallel than for calculation distance between planes we use the formula:

d |18 - (-6)|  =  |24|  =  24  = 4
22 + 42 + (-4)2 36 6

Answer: distance from plane to plane is equal to 4.

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