Explanation

(d) Let ${\overrightarrow{\mathbf{u}}}_{1}$ and ${\overrightarrow{\mathbf{u}}}_{\mathbf{2\ }}$be the initial velocities of the two particles and $\theta_{1}$ and $\theta_{2}$ be their angles of projection with the horizontal
The velocities of the two particles after time $t\ $are,
${\overrightarrow{\mathbf{v}}}_{1} = \left( u_{1}\cos\theta_{1} \right)\widehat{\mathbf{i}} + (u_{1}\sin{\theta_{1} - gt})\widehat{\mathbf{j}}$ and
${\overrightarrow{\mathbf{v}}}_{1} = \left( u_{1}\cos\theta_{1} \right)\widehat{\mathbf{i}} + (u_{2}\sin{\theta_{2} - gt})\widehat{\mathbf{j}}$
Their relative velocity is ${\overrightarrow{\mathbf{v}}}_{12} = {\overrightarrow{\mathbf{v}}}_{1} - {\overrightarrow{\mathbf{v}}}_{2}$
$= (u_{1}\cos\theta_{1} - u_{2}\cos\theta_{1})\ \widehat{\mathbf{i}} + (u_{1}\sin\theta_{1} - u_{2}\sin\theta_{2})\widehat{\mathbf{j}}$
Which is a constant. So the path followed by one, as seen by the other is a straight line, making a constant angle with the horizontal