A rotation is an orthogonal transformation C such that det C = +1. Prove that C does, in fact, rotate R^3 around an axis. Explicitly, given a rotation C, show that there exists a number J and points e 1, e 2 , e 3 with ei • ej = dij such that (Fig. 3.5) C(e1 ) = cos (J) e1 + sin (J) e2 , C(e2) = -sin (J) e1 + cos (J) e2 , C(e3 ) = e3
A rotation is an orthogonal transformation C such that det C = +1. Prove that C does, in fact, rotate R^3 around an axis. Explicitly, given a rotation C, show that there exists a number J and points e 1, e 2 , e 3 with ei • ej = dij such that (Fig. 3.5) C(e1 ) = cos (J) e1 + sin (J) e2 , C(e2) = -sin (J) e1 + cos (J) e2 , C(e3 ) = e3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
- A rotation is an orthogonal transformation C such that det C = +1. Prove
that C does, in fact, rotate R^3 around an axis. Explicitly, given a rotation C,
show that there exists a number J and points e 1, e 2 , e 3 with ei • ej = dij such
that (Fig. 3.5)
C(e1 ) = cos (J) e1 + sin (J) e2 ,
C(e2) = -sin (J) e1 + cos (J) e2 ,
C(e3 ) = e3
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
