# Distance between two planes

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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 + D_{1} = 0 and Ax + By + Cz + D_{2} = 0 is a plane equation, then distance between planes can be found using the following formula

d = | |D_{2} - D_{1}| |

√A^{2} + B^{2} + C^{2} |

## 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

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

d = | |18 - (-6)| | = | |24| | = | 24 | = 4 |

√2^{2} + 4^{2} + (-4)^{2} |
√36 | 6 |

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

Analytic geometry: Introduction and contentsDistance between two pointsMidpoint. Coordinates of midpointEquation of a lineEquation of a planeDistance from point to planeDistance between two planesDistance from a point to a line - 2-DimensionalDistance from a point to a line - 3-DimensionalAngle between two planesAngle between line and plane

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