# Homework 6, Due by email to TA Oct 30

This has lots of little math questions based on the lecture. They mostly require thinking, not just plugging in.

*(1 pt)*Write the 4x4 homogeneous matrix for a projection onto the viewplane {$x+2y+3z=6$} with the center of projection at (0,0,0).*(1 pt)*Write the 4x4 homogeneous matrix for a projection onto the viewplane {$z=0$} with the center of projection at (-1,0,0).*(1 pt)*Write the 4x4 homogeneous matrix for a uniform scale by 3 followed by a 3D translation by (1,1,1).*(2 pt)*Write the 4x4 homogeneous matrix for a 3D translation by (1,1,1) followed by a uniform scale by 3.*(1 pt)*Normalize the 3D Cartesian vector (1,2,3).*(2 pt)*Write the vector equation for rotating points by {$180^\circ$} about the axis (3,0,4).*(1 pt)*What does the point (0,2,0) rotate to?*(1 pt)*If {$a=(4,5,6)$} then write {$a\cdot p a$} as a matrix depending on {$a$} times {$p$}.*(1 pt)*Write {$a\times p$} ditto.- This
{$M=\begin{pmatrix}.6&0&.8\\0&\color{red}{0}&0\\.8&0&-.6\end{pmatrix} $}
is not a rotation matrix.
*(1 pt)*Give 2 rules for being a rotation matrix that it violates.*(1 pt)*Change {$m_{2,2}$}, highlighted in red above, to make {$M$} a rotation matrix.

*(2 pt)*This {$M=\begin{pmatrix}-1&0&0\\0&1&0\\0&0&-1\end{pmatrix} $} is a rotation matrix. What are the normalized axis and angle of rotation?