A nucleus moving with a velocity $\overrightarrow{v}$ emits an $\alpha$  particle . Let the velocities of the $\alpha$  particle and the remaining nucleus be ${\overrightarrow{v}}_1$ and ${\overrightarrow{v}}_2$ and their masses be m₁ and m₂.

 $\overrightarrow{v},{\overrightarrow{v}}_1$and ${\overrightarrow{v}}_2$ must be parallel to each other

None of the two of  $\overrightarrow{v},{\overrightarrow{v}}_1$and ${\overrightarrow{v}}_2$ should be parallel to each other

${\overrightarrow{v}}_1+{\overrightarrow{v}}_2$ must be parallel to $\overrightarrow{v}$

$m_1{\overrightarrow{v}}_1+m_2{\overrightarrow{v}}_2$ must be parallel to $\overrightarrow{v}$