For planes $$a_1x + b_1y + c_1z + d_1 = 0$$ and $$a_2x + b_2y + c_2z + d_2 = 0$$:
$$ \cos \theta = \frac{|a_1 a_2 + b_1 b_2 + c_1 c_2|}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}} $$
where $$\theta$$ is angle between normals.
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CAT Formulas
Three Dimensional Geometry
Angle between two planes
For planes $$a_1x + b_1y + c_1z + d_1 = 0$$ and $$a_2x + b_2y + c_2z + d_2 = 0$$:
$$ \cos \theta = \frac{|a_1 a_2 + b_1 b_2 + c_1 c_2|}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}} $$
where $$\theta$$ is angle between normals.
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