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

