(i) A particle \(A\) travels with a speed of \(6.5\text{ m s}^{-1}\) in the direction \(-5\mathbf{i}-12\mathbf{j}\). Find the velocity \(\mathbf{v}_A\) of \(A\).

(ii) A particle \(B\) travels with velocity \(\mathbf{v}_B=12\mathbf{i}-9\mathbf{j}\). Find the speed of \(B\).

Particle \(A\) starts from the point with position vector \(20\mathbf{i}-7\mathbf{j}\). At the same time particle \(B\) starts from the point with position vector \(-67\mathbf{i}+11\mathbf{j}\).

(iii) Find the position vectors \(\mathbf{r}_A\) and \(\mathbf{r}_B\) after \(t\) seconds.

(iv) Find the time when the particles collide and the position vector of the point of collision.