So I am making a raytracer following the very helpful online book of Gabriel Gambettta 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 except that he seems to know already what needs be done and is just asking about if his rationale is good.

Thanks