Look At Vector (LookAt Function Not Working For This)

Below is the picture of what I want to happen

Essentially I want to rotate the gun so that the green line (its GetActorRightVector()) is identical to the orange line. I’ve tried doing a look at rotation, but that doesn’t seem to work. I’ve tried a bunch of things, but can not get this… Any help is appreciated.

Basically I want the gun to rotate so its forward moves along the magenta line until it reaches the intersection of the magenta and orange.

Note: You can ignore the sphere and blue dot, those are there for other reasons.