---
title: 3D Mathematics
categories: session
geometry: margin=2cm
fontsize: 12pt
---

**Reading** Ma (2004) Chapter 2 + Appendix A

# Briefing

1.  **Recap** [Change of Basis]()
1.  **New** [Representations of 3D Motion]()
1.  (More on [3D Motion]())

# Exercises

Note.
Exercises in parentheses are optional.
Please skip these unless you have a lot of time.

All exercises are from Ma 2004 page 38ff

1. Exercise 2.1 a+d (b+c).  (See Definition A.12 page 446.)
1. (Exercise 2.2) (See Definition A.7 page 444 and A.29 page 454)
1. Exercise 2.3.  (See Definition A.13 page 447.)
1. ?? Exercise 2.4.  
1. Exercise 2.5.  
1. Exercise 2.6.  
   If you prefer, you can consider transformations in 3D instead,
   with the matrices
   $$
   R_1=
   \begin{bmatrix}
     \cos\theta & -\sin\theta & 0 \\
     \sin\theta & \cos\theta & 0 \\
     0 & 0 & 1 
   \end{bmatrix}
   \quad
   R_2=
   \begin{bmatrix}
     \sin\theta & \cos\theta & 0 \\
     \cos\theta & -\sin\theta & 0 \\
     0 & 0 & 1 
   \end{bmatrix}
   $$
   The relationship between the two matrices will be the same in 2D and 3D.

1. Exercise 2.7.  
1. Exercise 2.10.  

**TODO** From the textbook

# Debrief

Continue on [3D Mathematics]()