Particle \(A\) starts from the point with position vector \(3\mathbf{i}-2\mathbf{j}\). It moves with speed \(26\,\text{m s}^{-1}\) in the direction of the vector \(12\mathbf{i}+5\mathbf{j}\).

Particle \(B\) starts from the point with position vector \(67\mathbf{i}-18\mathbf{j}\). It moves with speed \(20\,\text{m s}^{-1}\) at an angle \(\alpha\) above the positive \(x\)-axis, where \(\tan\alpha=\frac34\).

The particles meet after \(t\) seconds. Find the value of \(t\) and the position vector of the point where they meet.