# How do you find the parametric equations of each line in space the line that intersects (4,5,-2) and is parallel to the z-axis?

$\vec{r} \left(t\right) = \left(\begin{matrix}4 \\ 5 \\ - 2\end{matrix}\right) + t \left(\begin{matrix}0 \\ 0 \\ 1\end{matrix}\right)$
any line that is parallel to the z axis has direction $\setminus \vec{d} = \hat{z} = \left(\begin{matrix}0 \\ 0 \\ 1\end{matrix}\right)$
$\vec{r} \left(t\right) = \left(\begin{matrix}4 \\ 5 \\ - 2\end{matrix}\right) + t \left(\begin{matrix}0 \\ 0 \\ 1\end{matrix}\right)$