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2. Consider the rotation matrix -1 R = 2√2 3 (a) Find an axis of rotation. This just means find an eigenvector n of R for the eigenvalue λ = 1 such that |n| = 1. Thus you are looking for a column vector n such that Rn = n. (b) Find the angle of rotation in degrees to two decimal points. Hint: Find any vector v that is perpendicular to n. Then calculate the angle between Rv and v.

2. Consider the rotation matrix -1 R = 2√2 3 (a) Find an axis of rotation. This just means find an eigenvector n of R for the eigenvalue λ = 1 such that |n| = 1. Thus you are looking for a column vector n such that Rn = n. (b) Find the angle of rotation in degrees to two decimal points. Hint: Find any vector v that is perpendicular to n. Then calculate the angle between Rv and v.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Consider the rotation matrix R 2√2 3 (a) Find an axis of rotation. This just means find an eigenvector n of R for the eigenvalue X = 1 such that |n| = 1. Thus you are looking for a column vector n such that Rn n. (b) Find the angle of rotation in degrees to two decimal points. Hint: Find any vector v that is perpendicular to n. Then calculate the angle between Rv and v.
Transcribed Image Text:2. Consider the rotation matrix R 2√2 3 (a) Find an axis of rotation. This just means find an eigenvector n of R for the eigenvalue X = 1 such that |n| = 1. Thus you are looking for a column vector n such that Rn n. (b) Find the angle of rotation in degrees to two decimal points. Hint: Find any vector v that is perpendicular to n. Then calculate the angle between Rv and v.
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