A particle \(P\) is moving in a straight line with speed \(26\) in the direction of the vector \(\begin{pmatrix}5\\-12\end{pmatrix}\).

(a) Find the velocity vector of \(P\).

When \(t=0\), \(P\) passes through a point \(A\) with position vector \(\begin{pmatrix}3\\6\end{pmatrix}\).

(b) Write down the position vector of \(P\) at time \(t\).

At the same time, a particle \(Q\) passes through a point \(B\). The position vector of \(Q\) at time \(t\) is \(\begin{pmatrix}8t-5\\2-25t\end{pmatrix}\). The distance between \(P\) and \(Q\) at time \(t\) is \(d\).

(c) Show that \(d^2=mt^2+nt+r\), where \(m,n,r\) are integers to be found.

(d) Hence show that \(P\) and \(Q\) do not collide.