3. A vector in a Cartesian coordinate system is represented by a column matrix: 1 13. (a) Rotate the vector counterclockwise by a ¼ turn about the z-axis. Write the column matrix that represents the new vector after rotation. (b) Write the rotation matrix for this transformation.
3. A vector in a Cartesian coordinate system is represented by a column matrix: 1 13. (a) Rotate the vector counterclockwise by a ¼ turn about the z-axis. Write the column matrix that represents the new vector after rotation. (b) Write the rotation matrix for this transformation.
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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3. A vector in a Cartesian coordinate system is represented by a column matrix: |1
[3]
(a) Rotate the vector counterclockwise by a 4 turn about the z-axis. Write the column matrix that
represents the new vector after rotation.
(b) Write the rotation matrix for this transformation.
4. In a Cartesian coordinate system, find the rotation matrix for rotating a vector about the y-axis
through an angle 0. Find the trace of this matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f6272ad-1a25-4a67-b389-4d6bf92e8dd2%2F90b8ac0c-d02a-4a0d-b18a-d589744a0ff1%2Fkxlw2c7_processed.png&w=3840&q=75)
Transcribed Image Text:[4]
3. A vector in a Cartesian coordinate system is represented by a column matrix: |1
[3]
(a) Rotate the vector counterclockwise by a 4 turn about the z-axis. Write the column matrix that
represents the new vector after rotation.
(b) Write the rotation matrix for this transformation.
4. In a Cartesian coordinate system, find the rotation matrix for rotating a vector about the y-axis
through an angle 0. Find the trace of this matrix.
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