Detailed Math To Generate Look Vector from Position, Velocity and Quaternions

I would like to generate the ECEF look vector of the satellite (Sentinel-1) BASED ON LEVEL-0 DATA so I can accurately map the SLC pixels I generate with my own image formation tool. I can compute something like a look vector from the cross product of the position vector and the velocity vector, but this is not accurate enough to compute accurate geo coordinates for the slant plane pixels. Sentinel-1-Level-1-Detailed-Algorithm-Definition.pdf Section 5.1 page 5-3 to 5-6 (56-60 of 159) is a description for computing the slant plane range vector. “u0” is similar to the position normal vector cross the velocity vector, but quite and certainly not “r”. Has anyone worked through how to compute “u0” in Matlab or Python code based on the position, velocity, and quaternions in the Level-0 product data? What are the actual steps to apply quaternions (whether directly or converted to pitch/roll/yaw) to help yield and accurate vector to help generate useful geo coordinates?