I have a position vector of a point in space and a quaternion for it's rotation. What i'm trying to calculate is a point too the left and a point to the right.

I have the position and rotation(quaternion) of the red dot. What I want is to get the position of the green dots. I have a float value for the distance I want these points to be.

With only the position and rotation is it possible to get a unit direction vector pointing left/right which I can multiply by my float value?

Edit: I also know the original direction vector.