Confusion in computing relative velocities between different coordinate frames [closed]

edit

I am writing a tree structure and I am trying to compute velocity between different frames on my own. But, I feel like my computation is wrong and was wondering if you guys can help me figure out what's wrong. 2

                                                      B                                  x 
                                                       \  (5,3,1)                        | 
                                                         \                         y <___|
                                                            1
                                                             \  (2,1,0)           x      
                                                               \                  |
                                                                2                 |____>Z

I was unable to attach an image, hence put that diagram above as an example. Note that frame 2 is rotated along roll w.r.t frame 1. Frame B and Frame 1 have same coordinate axis(X pointing up, +ve Y pointing to the left and +ve Z is coming out of the paper) and hence their total velocity will add up. So

relative velocity of B to 1 is (7,4,1).

But in the case of relative velocity of frame 1 and 2, frame 2 is rolled by +90 degrees and hence it's -ve Z axis is +ve Y axis of frame 1. I was asked to consider the velocities mentioned in that tree link as relative velocities between a child and a parent. That means, the relative velocity between frame 1 and 2 is (2,1,0).

My confusion is,

1. Does that mean that the X value 2, at the velocity vector is actually -Z value of frame 2?
2. How to compute the relative velocity between frame 2 to frame B.
3. Where can I learn more stuff about this?

I understand we need to include transformation matrices between frame 2 and 1 into account. But I am not sure how to incorporate it.

Any pointers that will help me understand this better will be greatly appreciated. Thank you!