Two particles of masses 5 gm and 15 gm are initially at rest at the origin. The lighter particle starts moving with velocity  $\overrightarrow{{\mathrm{v}}_1}=\left(3\hat{\mathrm{i}}-4\hat{\mathrm{j}}\right)\mathrm{m}/\mathrm{s}$ and simultaneously the heavier particle starts moving with velocity $\overrightarrow{{\mathrm{v}}_2}$. Find $\overrightarrow{{\mathrm{v}}_2}$ for which the centre of mass of the system always lies at the origin