Particle \(A\) is at the point with position vector \(\begin{pmatrix}2\\-5\end{pmatrix}\) at time \(t=0\) and moves with a speed of \(10\text{ m s}^{-1}\) in the same direction as \(\begin{pmatrix}3\\4\end{pmatrix}\).

(i) Given that \(A\) is at the point with position vector \(\begin{pmatrix}38\\a\end{pmatrix}\) when \(t=6\) s, find the value of \(a\).

Particle \(B\) is at the point with position vector \(\begin{pmatrix}16\\37\end{pmatrix}\) at time \(t=0\) and moves with velocity \(\begin{pmatrix}4\\2\end{pmatrix}\text{ m s}^{-1}\).

(ii) Write down, in terms of \(t\), the position vector of \(B\) at time \(t\) seconds.

(iii) Verify that particles \(A\) and \(B\) collide.

(iv) Write down the position vector of the point of collision.