rotating vector x around vector z

[ddr]

Is this how it should be done (rotating vector x around vector z for alpha degrees):
assumes |x|*|z|<>0
xonz=(scalar_product(z,x)/(|x|*|z|))*z;
y=x-xonz;
assumes |x|<>0
result=cos(alpha)*x+sin(aplha)*(|y|/|x|)*y;

[ddr]

actually y=croos_vector(z,(x-xonz))/|x-xonz|^2

[arcnets]

Not quite. I should say:

answer = xonz + y cos [alpha] + z/|z| X y sin [alpha].

Where X means vector product. And y = x - xonz.

Note: There should be a simpler form to this. Try yourself, please!