# Explicit calculation of 3x3 rotation matrix from combining three angle-unit axis rotations?

I need to remove dependence on a programming library from a computer application I'm working on and instead hand code a geometric operation. Please can you show explicitly (for someone with little experience of geometry) the primitive steps to calculate a 3x3 rotation matrix from the composition of three angle (in radians)- unit axis pairs?

Example input:

It depends on a couple of things: (1) What order do you do the rotations? i.e. Do you first rotate about $x$, then rotate the result about $y$, then the result of that about $z$, or vice versa, or something else? (2) Are your points represented as column vectors, $v=\begin{bmatrix}x\\y\\z\end{bmatrix}$ and you apply a matrix $A$ by computing $Av$, or are points row vectors $v=\begin{bmatrix}x&y&z\end{bmatrix}$ and you do $vA$? –  Rahul Aug 2 '12 at 22:26