- Particles \(P\) and \(Q\) move in a plane with constant velocities. At time \(t = 0\) the position vectors of \(P\) and \(Q\), relative to a fixed point \(O\) in the plane, are \(( 16 \mathbf { i } - 12 \mathbf { j } ) \mathrm { m }\) and \(( - 5 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m }\) respectively. The velocity of \(P\) is \(( \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and the velocity of \(Q\) is \(( 2 \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)
Find the shortest distance between \(P\) and \(Q\) in the subsequent motion.