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In Exercises 55–60, compute the angle between the two planes, de- fined as the angle 0 (between 0 and 1) between their normal vectors (Figure 9). 55. Planes with normals n¡ = (1, 0, 1), n2 = (-1, 1, 1) 56. Planes with normals n¡ = (1, 2, 1), n2 = (4, 1, 3) 57. 2x + 3y + 7z = 2 and 4x – 2y +2z = 4 58. х — Зу +2%3D 3 and 2x - 32 %3 4 59. 3(x – 1) – 5y +2(z – 12) = 0 and the plane with normal n = (1,0, 1) 60. The planc through (1, 0, 0), (0, 1, 0), and (0, 0, 1) and the yz-plane P2 Pi n2 ni FIGURE 9 By definition, the angle between two planes is the angle between their normal vectors.

In Exercises 55–60, compute the angle between the two planes, de- fined as the angle 0 (between 0 and 1) between their normal vectors (Figure 9). 55. Planes with normals n¡ = (1, 0, 1), n2 = (-1, 1, 1) 56. Planes with normals n¡ = (1, 2, 1), n2 = (4, 1, 3) 57. 2x + 3y + 7z = 2 and 4x – 2y +2z = 4 58. х — Зу +2%3D 3 and 2x - 32 %3 4 59. 3(x – 1) – 5y +2(z – 12) = 0 and the plane with normal n = (1,0, 1) 60. The planc through (1, 0, 0), (0, 1, 0), and (0, 0, 1) and the yz-plane P2 Pi n2 ni FIGURE 9 By definition, the angle between two planes is the angle between their normal vectors.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 34EQ
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In Exercises 55–60, compute the angle between the two planes, de- fined as the angle 0 (between 0 and 1) between their normal vectors (Figure 9). 55. Planes with normals n¡ = (1, 0, 1), n2 = (-1, 1, 1) 56. Planes with normals n¡ = (1, 2, 1), n2 = (4, 1, 3) 57. 2x + 3y + 7z = 2 and 4x – 2y +2z = 4 58. х — Зу +2%3D 3 and 2x - 32 %3 4 59. 3(x – 1) – 5y +2(z – 12) = 0 and the plane with normal n = (1,0, 1) 60. The planc through (1, 0, 0), (0, 1, 0), and (0, 0, 1) and the yz-plane P2 Pi n2 ni FIGURE 9 By definition, the angle between two planes is the angle between their normal vectors.
Transcribed Image Text:In Exercises 55–60, compute the angle between the two planes, de- fined as the angle 0 (between 0 and 1) between their normal vectors (Figure 9). 55. Planes with normals n¡ = (1, 0, 1), n2 = (-1, 1, 1) 56. Planes with normals n¡ = (1, 2, 1), n2 = (4, 1, 3) 57. 2x + 3y + 7z = 2 and 4x – 2y +2z = 4 58. х — Зу +2%3D 3 and 2x - 32 %3 4 59. 3(x – 1) – 5y +2(z – 12) = 0 and the plane with normal n = (1,0, 1) 60. The planc through (1, 0, 0), (0, 1, 0), and (0, 0, 1) and the yz-plane P2 Pi n2 ni FIGURE 9 By definition, the angle between two planes is the angle between their normal vectors.
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