OnlineMSchool
Study of mathematics online.
Study math with us and make sure that "Mathematics is easy!"

Angle between two planes

Angle between two planes
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 + C12A22 + 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)242 + 32 + 02 3625 30 3
Ответ: косинус угла между плоскостями равен
cos α
2 .
3

Add the comment

0