Convert two orthogonal unit vectors into euler vector

Question

I have two orthogonal unit vectors that would correspond to an orientation of the Z and Y axes. I want to convert this to a rotation/Euler vector.

In other words, I want to convert between two orthogonal unit vectors into an Euler vector.

Answer 1

I think I could use the cross product to get the third axis. These three unit vectors then form a basis and can form a rotation matrix where each vector forms a column of the matrix.

Then one can use a formula to convert from the rotation matrix to the euler vector.