The coordinates of first projectile as seen from the second projectile are
X = x1 - x2
= u1cosθ1 t - u2cosθ2 t
X = (u1cosθ1 - u2cosθ2)t
Y = y1 - y2
= u1sinθ1 t - 1/2 gt2 - (u2sinθ2 t - 1/2 gt2)
Y = (u1 sin θ1 - u2sin θ2)t
∴ = a constant, say m
This equation is of the form Y = mX, which is the equation of a straight line. Thus the path of a projectile as seen from another projectile is a straight line.