﻿﻿ Math.by - The angle between planes.

The angle between planes.

Enter the equations of the planes:

x + y + z + = 0

and

x + y + z + = 0

The angle between planes is:

in degrees =

Theory

If two planes intersect, they intersect in a straight line. This line divides each into two half-plane.

Figure formed by two half-planes and the line is called a dihedral angle. In this straight - this is the edge angle, the half-plane - it faces the corner.

Dihedral angle is measured by the linear, ie the angle formed by two beams perpendicular to the edge and corner of their respective faces.

The two crossed the plane formed by two pairs of adjacent angles. The smaller of adjacent angles is called the angle between the planes.

Let the intersecting planes set by the following equations:

$A_1 x+B_1 y+C_1 z+D_1=0$ and $A_2 x+B_2 y+C_2 z+D_2=0$

then the angle between the planes is calculated as follows:

$\phi = \arccos{\frac{A_1 A_2 + B_1 B_2 + C_1 C_2}{\sqrt{(A_1^2+B_1^2+C_1^2)(A_2^2+B_2^2+C_2^2)}}}$

References