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Angle between two planes

Statement. Find the angle between the horizontal plane z = 0 and plane Q: x + z = 0.

Step-by-step solution

1. The angle between two planes is the angle between their normals.
2. Normal of the horizontal plane: n1 = (0, 0, 1). Normal of Q: n2 = (1, 0, 1).
3. cos a = |n1 . n2| / (|n1| |n2|) = 1 / sqrt(2).
4. a = 45 degrees.

Result

45 degrees.

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