According to the law of conservation of linear momentum, the total momentum of the system remains conserved if no external force acts on it. Initial momentum = Final momentum $\vec{P}_i = \vec{P}_f$ $M \vec{v} = m_1 \vec{v}_1 + m_2 \vec{v}_2$ Given, the ratio of masses is $m_1 : m_2 = 1 : 5$. So, $m_1 = \frac{M}{6}$ and $m_2 = \frac{5M}{6}$, where $M$ is the total mass. $M(20\hat{i} + 25\hat{j} - 12\hat{k}) = \frac{M}{6} (100\hat{i} + 35\hat{j} + 8\hat{k}) + \frac{5M}{6} \vec{v}_2$ Dividing both sides by $M$ and multiplying by $6$, we get: $6(20\hat{i} + 25\hat{j} - 12\hat{k}) = (100\hat{i} + 35\hat{j} + 8\hat{k}) + 5\vec{v}_2$ $120\hat{i} + 150\hat{j} - 72\hat{k} = 100\hat{i} + 35\hat{j} + 8\hat{k} + 5\vec{v}_2$ $5\vec{v}_2 = (120 - 100)\hat{i} + (150 - 35)\hat{j} + (-72 - 8)\hat{k}$ $5\vec{v}_2 = 20\hat{i} + 115\hat{j} - 80\hat{k}$ $\vec{v}_2 = 4\hat{i} + 23\hat{j} - 16\hat{k}$