Considering that I have a vector A, and after an arbitrary rotation I get vector B. I want to use this rotation operation in others vectors as well, but I'm having problems in doing that.

My idea do that is to calculate the perpendicular vector C of the plane AB (by calculating AxB). This vector C is the axis that I'll need to rotate. To discover the angle I used the dot product between A and B, the acos of the dot product will return the lowest angle between A and B, the angle ang. The rotation I need to do is then: -rotate *ang*º around the C axis.

The problem is that I dont know if this rotation is a CW or CCW rotation, since the cos of the dot product does not give me information of the sign of the angle. There's a tip discover that in 2D ( A.x * B.y - A.y * B.x) that you can use to discover if the vector A is at left/right of vector B. But I dont know how to do this in 3D space. Can anyone help me?