Particle \(A\) is initially at the point with position vector \(\begin{pmatrix} 3 \\ -2 \end{pmatrix}\) and moves at a constant speed of \(26\) m / s in the direction of the vector \(\begin{pmatrix} 12 \\ 5 \end{pmatrix}\). Find the position vector of \(A\) after \(t\) seconds.
At the same time when particle \(A\) starts moving, particle \(B\) starts moving from the point with position vector \(\begin{pmatrix} 67 \\ -18 \end{pmatrix}\). It travels with speed \(20\) m / s at an angle of \(\alpha\) above the positive \(x\) -axis, where \(\tan \alpha = \frac{3}{4}\). 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.
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