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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 formulaIf 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
Examples of tasks with distance between two planesExample 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 = 0As planes are parallel than for calculation distance between planes we use the formula:
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  2DimensionalDistance from a point to a line  3DimensionalAngle between two planesAngle between line and plane
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