prove(mathematically) that path of a projectile as seen from another projrctile is a straight line

eq of path of projectile is s=ucos@ -gt²/2

if two projectiles are projected from horizontal ground with different initial velocity and angle....both these quantities are known then at any time t

coordinates of A,  S1=(UacosA)t i - gt²/2 j

coordinates of B, S2=(UbcosB)t i - gt²/2j

 coordinates of A wrt to B is S2-S1=t(UacosA-UbcosB)i + 0 j

            Xi + Yj = kt i + 0j                                     (UacosA-UbcosB = constant=k)

  ie X=kt  is a straight line