Solution Found!
(a) Prove that the two-dimensional rotation matrix (Eq.
Chapter 1, Problem 8P(choose chapter or problem)
(a) Prove that the two-dimensional rotation matrix (Eq. 1.29) preserves dot products. (That is, show that .)
(b) What constraints must the elements (Ri j) of the three-dimensional rotation matrix (Eq. 1.30) satisfy, in order to preserve the length of A (for all vectors A)?
Reference equation 1.30
,
Reference equation 1.29
.
Questions & Answers
QUESTION:
(a) Prove that the two-dimensional rotation matrix (Eq. 1.29) preserves dot products. (That is, show that .)
(b) What constraints must the elements (Ri j) of the three-dimensional rotation matrix (Eq. 1.30) satisfy, in order to preserve the length of A (for all vectors A)?
Reference equation 1.30
,
Reference equation 1.29
.
ANSWER:Step 1 of 5
In part (a) we have to prove that using given two dimensional rotation matrix equations.
Given the two dimensional rotation matrix is,
Using the above equations,