So I am making a raytracer following the very helpful [online book of Gabriel Gambettta][1] but I stumble on the rotation matrix part. 

My linear algebra background is 3Blue1Brown video series "The essence of Linear Algebra".

I simulate a camera placed at the origin that's looking forward ie whose direction is the vector `{0,0,1}`. 
Let's say I am given another camera direction with direction `{a,b,c}`. 
From what I understand if I find the rotation matrix R that takes as an input `{0,0,1}` and spits out a normalized `{a,b,c}` as an output. 
Then I can apply that rotation matrix to all my rays in order to rotate them. 
I can't get my head around on how to find R. Any help/explanation/correction much welcome.

I am in a similar situation than [the person aksing this question][2] except that he seems to know already what needs be done and is just asking 
about if his rationale is good.

Thanks

EDIT : The answer below is valid considering how I framed my problem but note that if you were like me trying to compute a camera to world rotation matrix and expected the viewport of your camera to follow along, you need an additional step because the answer below only gives you a shear matrix. In order to get a rotation matrix you need to comput the `upVector` with `normalize(cross_product(rightVector, forwardVector))` (in a right hand system) and feed its coordinates into the matrix instead of `{0,1,0}`


  [1]: https://www.gabrielgambetta.com/computer-graphics-from-scratch/05-extending-the-raytracer.html
  [2]: https://computergraphics.stackexchange.com/questions/10613/transforming-a-ray-from-camera-space-to-world-space?rq=1