Find both the vector equation and the parametric equations of the line through $$ (0,0,0) $$ that is parallel to the line $$ \mathbf{r}=\langle 3-2 t, 9+5 t, 2+3 t\rangle $$, where $$ t=0 $$ corresponds to the given point. The vector equation is $$ \langle x, y, z\rangle=\langle 0,0,0\rangle+t\langle-2,5,3\rangle $$. The parametric equations are $$ x=\square, y=\square, z=\square $$. (Use the answer from the previous step to find this answer.)

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Using the vector equation $$\langle x, y, z \rangle = \langle 0, 0, 0 \rangle + t\langle -2, 5, 3 \rangle$$, we can derive the parametric equations by equating each component:

$$
\begin{cases}
x = 0 + (-2)t = -2t \
y = 0 + 5t = 5t \
z = 0 + 3t = 3t \
\end{cases}
$$

**Parametric Equations:**
$$
\begin{aligned}
x &= -2t, \
y &= 5t, \
z &= 3t.
\end{aligned}
$$
The parametric equations are: $$ \begin{cases} x = -2t, \ y = 5t, \ z = 3t. \end{cases} $$

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