Distance from point to plane.
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Definition.
The distance from a point to a plane is equal to length of the perpendicular lowered from a point on a plane.Distance from point to plane formula
If Ax + By + Cz + D = 0 is a plane equation, then distance from point M(Mx, My, Mz) to plane can be found using the following formula:
| d = | |A·Mx + B·My + C·Mz + D| |
| √A2 + B2 + C2 |
Examples of tasks with distance from point to plane
Example 1.
To find a distance between plane 2x + 4y - 4z - 6 = 0 and point M(0, 3, 6).
Solution. Let's use the formula
| d = | |2·0 + 4·3 + (-4)·6 - 6| | = | |0 + 12 - 24 - 6| | = | |- 18| | = 3 |
| √4 + 16 + 16 | √36 | 6 |
Answer: Distance from point to plane is equal to 3.
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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