Rotation around Axis(R3) to Rotation around Cartesian-Axes(r1, r2, r3))

Jul 2018

my problem is as follows:

I have the angle between two vectors in R3, lets say it's q.

vector1: (v1, v2, v3)
vector2: (w1, w2, w3)

How can I figure out, how to rotate vector1 around X, then Y, then Z, to create the same rotation as the angle-rotation around vector1's and vector2's normal vector would give me to reach vector2?

Let's assume both vectors are unitized and are situated at the origin.

Any ideas?