Here's the short version: multiply your source vector by a 3d rotation matrix. Zaxo's snippet is nifty, but not quite sufficient as it doesn't do matrix math.
The extra complexity that comes with moving from 2d rotations to 3d rotations is the fact that, in 3d, you don't really have a canonical axis to rotate around. In the x-y plane, when you do a rotation by r radians, you pretty much have to rotate around the z axis. In 3d space, you can rotate around the x, y, or z axis, or around an arbitrary vector (if that gives you problems, think of it as rotating around several canonical axes at once). So you can't easily describe a 3d rotation with a single parameter; you basically need a matrix (or a quaternion, but let's not go there).
Are you posting in the right place? Check out Where do I post X? to know for sure.
Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
<code> <a> <b> <big>
<blockquote> <br /> <dd>
<dl> <dt> <em> <font>
<h1> <h2> <h3> <h4>
<h5> <h6> <hr /> <i>
<li> <nbsp> <ol> <p>
<small> <strike> <strong>
<sub> <sup> <table>
<td> <th> <tr> <tt>
Snippets of code should be wrapped in
<code> tags not
<pre> tags. In fact, <pre>
tags should generally be avoided. If they must
be used, extreme care should be
taken to ensure that their contents do not
have long lines (<70 chars), in order to prevent
horizontal scrolling (and possible janitor
Want more info? How to link
or How to display code and escape characters
are good places to start.