1.6: Vector from magnitude and simultaneous equations

The vector $\mathbf{v}$ has a magnitude of $39$ units and is in the same direction as $\begin{pmatrix} -12 \\ 5 \end{pmatrix}$. Write $\mathbf{v}$ in the form $\begin{pmatrix} a \\ b \end{pmatrix}$, where $a$ and $b$ are constants.

Vectors $\mathbf{p}$ and $\mathbf{q}$ are such that $\mathbf{p} = \begin{pmatrix} r+s \\ r+6 \end{pmatrix}$ and $\mathbf{q} = \begin{pmatrix} 5r+1 \\ 2s-1 \end{pmatrix}$, where $r$ and $s$ are constants. Given that $2\mathbf{p} + 3\mathbf{q} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}$, find the value of $r$ and of $s$.