Given, mass of first body $\left(m_1\right)=3 \mathrm{~kg}$
$$
\begin{aligned}
\text { Velocity of first body }\left(v_1\right) & =(2 \hat{i}+3 \hat{j}+3 \hat{k}) \mathrm{m} / \mathrm{s} \\
\text { Mass of second body }\left(m_2\right) & =4 \mathrm{~kg} \\
\text { Velocity of second body }\left(v_2\right) & =(3 \hat{i}+2 \hat{j}-3 \hat{k}) \mathrm{m} / \mathrm{s}
\end{aligned}
$$
According to law of conservation of linear momentum,
$$
\begin{array}{lc}
& m_1 v_1+m_2 v_2=\left(m_1+m_2\right) v \\
\Rightarrow & (2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) 3+(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}) 4=(4+3) v \\
\Rightarrow & 6 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}+9 \hat{\mathbf{k}}+12 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}-12 \hat{\mathbf{k}}=7 \mathrm{~V} \\
\Rightarrow & 18 \hat{\mathbf{i}}+17 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}=7 \mathrm{~V}
\end{array}
$$

$$
\Rightarrow \quad v=\frac{1}{7}(18 \hat{\mathbf{i}}+17 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})
$$