Your assumption, that crossing lasers will make them visible, is unfortunately incorrect. I’m afraid the photo has led you astray. In order to see light, there needs to be something present to direct the light toward your eyes. In your photo, the laser beams are not simply in free, clear air. It appears that the beams are grazing along a table. Moreover, it looks like there is some kind of frosted glass cylinder that the beams are lighting up at the focus (see how the beams look far more diffuse after the cylinder, and the blue light even looks shadowed). In any case, there is plenty of scattering happening, redirecting some light to the camera. Do this experiment in vacuum, with no cylinder and no table, and you won’t see a thing. The light from the cylinder looks white because of the mixture of several colors across the spectrum, and it looks uniform on the cylinder because the camera is probably saturating.