Rotating two vector by the same rotation matrix Let's say we have two sets of vectors $A$, $B$ and $A'$, $B'$. These vectors are connected such that
$A' = R. A$, and 
$B'=R.B$.  Where R is a $3D$ rotation matrix.
Now let's assume we know $A$, $B$ and $A'$, $B'$. 
Then is there any way to know $R$?
If yes, then what should be the approach to find it.

As long as $A$ and $B$ are linearly independent, then $R$ is uniquely
determined. For $R(A\times B)=A'\times B'$, and as $A$, $B$, $A\times B$
form a basis for $\Bbb R^n$ then $R$ is determined by its action on these
three vectors.
