3.29: Meeting point of two particles

Particle $A$ starts from $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$ and travels at $26\,\mathrm{ms}^{-1}$ in the direction of $\begin{pmatrix} 12 \\ 5 \end{pmatrix}$. Find the position vector of $A$ after $t$ seconds.

Particle $B$ starts from $\begin{pmatrix} 67 \\ -18 \end{pmatrix}$ at the same time, with speed $20\,\mathrm{ms}^{-1}$ at angle $\alpha$ above the positive $x$-axis where $\tan\alpha = \dfrac{3}{4}$. Find the position vector of $B$ after $t$ seconds.

Hence find the time at which $A$ and $B$ meet, and the position where this occurs.