rotational-matrices

How can I find the unit vector between a point and a line?

I have three known 3-Dimensional points: A, B, and C. Addtionally, I have a fourth point, X. X lies on vector AB such that vector CX is perpendicular to vector AB. So AB · CX = 0 How do I find the unit vector of CX? The use-case here is that I am constructing a (translated) rotational matrix, where the origin is A, the z-axis pass...