Angle between two planes
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Definition.
The angle between planes is equal to a angle between their normal vectors.Definition.
The angle between planes is equal to a angle between lines l1 and l2, which lie on planes and which is perpendicular to lines of planes crossing.Angle between two planes formulas
If A1x + B1y + C1z + D1 = 0 and A2x + B2y + C2z + D2 = 0 are a plane equations, then angle between planes can be found using the following formula
| cos α = | |A1·A2 + B1·B2 + C1·C2| |
| √A12 + B12 + C12√A22 + B22 + C22 |
Examples of tasks with angle between two planes
Example 1.
To find an Angle between planes 2x + 4y - 4z - 6 = 0 and 4x + 3y + 9 = 0.
Solution. Let's use the formula:
| cos α = | |2·4 + 4·3 + (-4)·0| | = | |8 + 12| | = | 20 | = | 2 |
| √22 + 42 + (-4)2√42 + 32 + 02 | √36√25 | 30 | 3 |
| Answer: the cosine of the angle between the planes is cos α = |
2 | . |
| 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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