# Calculating normal vector to a rotated plane

Forgive me if this isn't well phrased, it's been a while since I've done any maths!

I have a 2d image whose central point is located at the world origin, and it is in the plane $z = 0$.

If I rotate the image $\alpha$ degrees about the $z$-axis and $\beta$ degrees about the $x$-axis, how can I calculate the normal vector to the plane the image is now on?

If I understand you correctly, the original normal is $(0,0,1)^T$. Rotating this around the z-axis has no effect, and rotating by β degrees around the x-axis will rotate the normal similarly, so the normal will be $(0,-\sinθ,\cosθ)^T$, where $θ=\frac{π}{180}β$. –  copper.hat Aug 13 '12 at 16:17