How do I calculate roll, pitch, yaw from a unit vector?

How do I calculate roll, pitch, yaw from a unit vector?

I am provided a unit vector giving a direction in x, y, z coordinates, and
that the roll is defined as about the x axis, pitch around y, yaw around
z. I'm trying to determine how to calculate roll, pitch, and yaw given the
unit vector. I can see that the information should be there, but after
looking in to it for a bit, I've been unable to find the correct method of
doing this. How do I go about doing this?