as per explanation in the document. I'm looking for the matrix transformation M2 express in G frame.

Given matrix M1, and vectors V1 and V2, I want to solve for matrix M2. VI- #3- Note: Translation for all of these is 0,0,0. I just drew them separately for visibility. We have a Global frame coordinate system (G). Everything in this problem will be expressed in the Global frame G. We are given a coordinate system CS1 expressed as matrix MI in the global coordinate frame G. Therefore, we have a vector VI along the ' axis of C51. We are also given a vector V2 (expressed in the global frame G). We want to rotate CS1, in the plane made by V1 & V2, by the value of the angle of V1 to V2. What is the new matrix M2 (expressed in the global frame G)? I need i1, 12, i3, j1, j2, j3, k1, k2, k3 (of the matrix MZ) ANOTHER WAY TO DESCRIBE THE SAME PROBLEM: Since one person misunderstood the problem statement, I want to describe it in a different manner. We have a Global frame coordinate system (G). Everything in this problem will be expressed in the Global frame G. We are given a coordinate system C51 expressed as matrix M1 in the global coordinate frame G. We have a vector VI along the I' axis of C51 (expressed in the global frame G). We also have a vector V2 (expressed in the global frame G]. - We want to rotate CS1, in the plane made by VI & V2 so that V1 (ie. z') becomes aligned with V2. - What is the new matrix M2 (expressed in the global frame G)? I need il, i2, i3, j1, j2, j3, k1, k2, k3 ( of the matrix M2) To simplify it, if the problem was simply a 2D problemn, it would be as follows: MI- VI - L CSI In the 20 representation above, we are assuming that the Y axes of both C$1 and CS2 are aligned, so the only rotations happen in the ZX plane. This is only a representation to aid visualization. In reality, these matrices are in full 30, so rotation happens along all axes