I know that we can perform algebric operations in the so(3) plane. Let us take $R_1,R_2$ and $R_3$ as rotation matrices in SO(3) plane. ^v: vector representation of skew-symmetric matrix.
Vector from $R_1$ to $R_2$ in s0(3) is a skew-symmetric matrix $=(R_2^TR_1-R_1^TR_2)^V$.
Vector from $R_2$ to $R_3$ in s0(3) is a skew-symmetric matrix $=(R_3^TR_2-R_2^TR_3)^V$.
So can I say vector from $R_1$ to $R_3$ in s0(3) is a skew-symmetric matrix $=(R_3^TR_1-R_1^TR_3)^V$? Is $(R_2^TR_1-R_1^TR_2)^V+(R_3^TR_2-R_2^TR_3)^V=(R_3^TR_1-R_1^TR_3)^V$?