Can light 'reflect' off other light(s)?

I had an idea for a holographic projector where a U shaped device filled with L.E.D's that have been modified to output light like a laser.

An individual dot/pixle is created by reflecting three beams or rather where the 'laser beams' intersect

Is this actually possible? That you could see a hovering dot if three beams of light hit each other?

Like a 'laser' wavelength not normal light

If you look at a simple mechanis of reflection which is that a light wave falls on a mirrored surface, induces oscillations onto its electrons,  which in turn, will radiate light back ... and then there is the incindence angle = reflection angle

however a light wave doesnt have any electrons to giv its energy too, so light might not be able to reflect light!

however, i could be wrong!