Speed of light travel
But then the speed of light is universal constant regardless of the motion of its frame of reference, so shouldn't their relative velocity be $c$? What is their relative velocity and how?
EDIT Upon further review (special thanks to Alfred's comment), I think my original answer is incorrect. It turns out that the question of relative velocities of photons moving in the same direction is a meaningless question. The reason is as follows.
For two objects A
and B
moving as such,
v u -------> A -------> B ------------------ (ground)
The velocity of B
in A
's frame is then
$$
u'=\frac{u-v}{1-\frac{uv}{c^2}}
$$
Notice the denominator? For $u=v=c$, this is zero and we get 0/0 which is an undefined operation, hence the meaningless question.
Do objects moving at the speed of light obey law of addition of velocities?
Not exactly. The Galilean velocity addition, $s=u+v$ does not hold for large-velocity objects. We use the "composition law", $$ s=\frac{u\pm v}{1\pm\frac{uv}{c^2}} $$ where $\pm$ depends on directions/frames. If $uv\ll c^2$, then this does reduce to the Galilean transformation.