special relativity - Speed of light travel

I have just started special theory of relativity. The limiting speed known as speed of light fascinated me most. I asked my teacher:

Consider two massless objects moving in the same direction at the speed of light. What would be their relative velocity w.r.t each other?

My teacher tells me that their relative velocity would be zero. 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? Do objects moving at the speed of light obey law of addition of velocities?

Answer

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.