A particle \(P\) is moving with a velocity of \(20\text{ m s}^{-1}\) in the same direction as \(\binom34\).

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

At time \(t=0\), \(P\) has position vector \(\binom12\) relative to a fixed point \(O\).

(ii) Write down the position vector of \(P\) after \(t\) seconds.

A particle \(Q\) has position vector \(\binom{17}{18}\) relative to \(O\) at time \(t=0\), and has velocity vector \(\binom8{12}\text{ m s}^{-1}\).

(iii) Given that \(P\) and \(Q\) collide, find the value of \(t\) and the position vector of the point of collision.