The Angle between two Planes; an application of the Angle between two Lines |
Problem: |
||
A diagram of this is shown on the right. | is a normal vector to Plane
1 is a normal vector to Plane 2. θ is the angle between the two planes. By simple geometrical reasoning; angle between two planes equals angle between their normals. |
|
The angle, θ, between the two normal vectors can be easily found using 'the angle between two lines' method. From the equations to the two given planes,.[3, 4, 0] = 5 and, .[1, 2, 3] = 6, the normal to Plane 1 is parallel to the vector [3, 4, 0] and the normal to Plane 2 is parallel to the vector [1, 2, 3]. The angle between the two normals is therefore, the angle between the two vectors [3, 4, 0] and [1, 2, 3]; [3, 4, 0] . [1, 2, 3] = | [3, 4, 0] | × | |cosα
|
||