Vector Equations of Lines 3

Find the distance of the point $A(-3,1)$ to the line
$$\displaystyle{\vec{r}=\begin{bmatrix}1\\2\end{bmatrix}+\lambda \begin{bmatrix}-2\\3\end{bmatrix}}$$

using the method outlined below.

1. Find an expression for an arbitrary point $D$ on the given line.
2. Using the expression you’ve produced, find a general expression for the vector $\overrightarrow{AD}$.
3. Where $\vec{b}$ is the direction vector of the given line, use the dot product $\overrightarrow{AD}\cdot\vec{b}$ to find the coordinates of the point on the line closest to $A$. Hence, find the distance from $A$ to the line.