In this question, time is in seconds. (a) At time \(t=0\), particle \(P\) starts from the point with position vector \(-30 \mathbf{j}\). \(P\) travels with speed \(58 \mathrm{~ms}^{-1}\) in the direction \(20 \mathbf{i}+21 \mathbf{j}\). Find the position vector of \(P\) at time \(t\).

(b) Also at time \(t=0\), particle \(Q\) starts from the point with position vector \(-10 \mathbf{i}+18 \mathbf{j}\). \(Q\) travels with speed \(75 \mathrm{~ms}^{-1}\) at an angle \(\alpha\) above the positive \(x\)-axis, where \(\tan \alpha=\frac{7}{24}\). Find the position vector of \(Q\) at time \(t\).

(c) Determine whether \(P\) and \(Q\) collide.