The matrix P that multiplies ( x, y, z) to give ( z, x, y) is also a rotation matrix.Find P and P3. The rotation axis a = (l, 1, 1) doesn't move, it equals Pa. What is the angle of rotation from v = (2, 3, -5) to Pv = (-5, 2, 3)?
The matrix P that multiplies ( x, y, z) to give ( z, x, y) is also a rotation matrix.Find P and P3. The rotation axis a = (l, 1, 1) doesn't move, it equals Pa. What is the angle of rotation from v = (2, 3, -5) to Pv = (-5, 2, 3)?
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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The matrix P that multiplies ( x, y, z) to give ( z, x, y) is also a rotation matrix.
Find P and P3. The rotation axis a = (l, 1, 1) doesn't move, it equals Pa. What is the angle of rotation from v = (2, 3, -5) to Pv = (-5, 2, 3)?
Expert Solution
Step 1
We have to find the matrix P such that where P is the rotation matrix. Then, we have to
find the matrix .
We know that a rotation matrix is a square matrix whose all entries are real numbers. The determinant
of a rotation matrix is equal to 1.
Step 2
Now,
Therefore, .
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