What is the acute angle between the two planes with normal vectors n1 = (1, 1, 0) and n2 = (0, 1, 1)?
Answer and explanation
Correct answer: A. pi/3 radians (60 degrees)
- Step 1: Dot product n1 . n2 = 10 + 11 + 01 = 1. Magnitudes |n1| = sqrt(1^2 + 1^2) = sqrt(2); |n2| = sqrt(2). Step 2. cos(theta) = 1 / (sqrt(2) sqrt(2)) = 1/2. Thus theta = arccos(1/2) = pi/3 radians (60 degrees). Answer: pi/3 radians (60 degrees). Why not the others: The angle between two planes equals the angle between their normal vectors.
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