Rapidly spinning laser to create one-lined image

If the laser wants 3v, then I just add the appropriate resistor right?

Wrong.

why can't it be mentioned in one or 2 sentences? Like this, "That won't work because X, Y, Z"

This won't work because a laser presents a varying impedance to the thing driving it and so a simple resistor will not be able to give it the constant current it needs.