The projection of $\vec{a}$ on $\vec{b}$ is given by:

$\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = 0$

Since $\vec{b}$ is a non-zero vector, $|\vec{b}| \neq 0$. Therefore, $\vec{a} \cdot \vec{b} = 0$.

We know that $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos{\theta}$, where $\theta$ is the angle between $\vec{a}$ and $\vec{b}$.

So, $|\vec{a}| |\vec{b}| \cos{\theta} = 0$. Since $\vec{a}$ and $\vec{b}$ are non-zero vectors, $|\vec{a}| \neq 0$ and $|\vec{b}| \neq 0$.

Therefore, $\cos{\theta} = 0$.

The angle $\theta$ for which $\cos{\theta} = 0$ is $\theta = \frac{\pi}{2}$.