3. Affine transformations in three dimensions

Everything works exactly the same: For x$= (x,y,z)$, $\hat{\mbox{\bf x}}$ is $(x,y,z,1)$. The extended matrix of an affine transformation $T:$   R$^3 \rightarrow$   R$^3$ is $4 \times 4$.

Application 3.1 . Rotations in R$^3$ about axes that do not go through the origin.

Application 3.2 . Reflections in R$^3$ in plane mirrors that do not go through the origin.