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The Angle Between Two Planes

As illustrated in the diagram below, the angle between two planesandis equal to the angle between the normals to the planesand

 

The components of the normal appear in the cartesian equation of the plane, because ifis any point in the plane,is any fixed point and the normal isthenwhereandare the position vectors ofandrespectively. This results in the equation of the planeand the normal can be read off:

Thus given the cartesian equations of two planes, we can read off the normalsandand the angle between the planes is given by

Example: Planesandare given byandThe normalsandare given byand

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