# Let $Z$ be standard normal can we find a pdf of $(Z_1,Z_2)$ where $Z_1=Z \cdot 1_{S},Z_2=Z \cdot 1_{S^c}$

Let $S \subset \mathbb{R}$ and let $Z$ be a standard normal random variable.
Let
\begin{align}
Z_1&=Z \cdot 1_{S},\\
Z_2&=Z \cdot 1_{S^c},
\end{align}
where $1_S$ is an indicator function and $S=[-a,a]$ for some $a>0$.

Can we find the distribution of ${Z_1}$ and $(Z_1,Z_2)$ and $Z_1 |Z_2$?

Thanks.