How to calculate the rotation parameters of one vector to another?

Question

Linear algebra

There is a certain family of vectors. One of them is called "master". We know its parameters.
We want to rotate the whole family along with the main one.
We know where the main vector should "look" after the turn.

How to compose a rotation matrix for such a case? We can only rotate around the axes, and it doesn't seem to have anything to do with the angle between the two vectors.

For example, there is a main vector (0, 250, 0), we want to make it point in the same direction as the vector (100, 100, -75). How to calculate parameters?

Answer 1

- Normalize the source and destination vectors, it will be easier.

We can only rotate around the axes

- consider projections of vectors on the XY, XZ, YZ planes; the angle between vectors on the plane is easy to calculate, turn to this angle.