# Homework 5, due Wed Oct 2, 2013 (RPI, ECSE-4750)

Hand in your solution on RPILMS. Each team should submit their solution under only 1 student's name. The other student's submission should just name the lead student. (This makes it easier for us to avoid grading it twice.) For programming exercises, hand in code and screen dumps. We won't run your code, but will use the screendumps to judge how it worked.

1. (2 pts) Give the matrix M that has this property: for all vectors p, {$Mp = \begin{pmatrix}2\\3\\4\end{pmatrix} \times p$}.
2. (2 pts) Give the matrix M that has this property: for all vectors p, {$Mp = \left(\begin{pmatrix}2\\3\\4\end{pmatrix} \cdot p \right) \begin{pmatrix}2\\3\\4\end{pmatrix}$}.
3. (6) Combining two 3D rotations gives a new rotation. So, imagine that you rotate by {$90^o$} about the X-axis, and then rotate by {$90^o$} about the Y-axis. Give the normalized axis and angle of the single rotation that this corresponds to.
You may use any mathematical technique that you please. One way is to find the matrices for the two rotations, multiply them, and then extract the axis and angle from the resulting matrix. You may use your favorite matrix SW.
Don't just give an answer; tell us how you did it.
4. (10) Do Exercise 4.52 on page 155.

(Total: 20 points.)