I have four vectors $A$, $B$, $A'$, and $B'$. Now $A$ and $B$ are in one plane and $A'$ and $B'$ are in another plane.
Now is there any way so that I can get the components of $A'$ in the same direction of $A$ or $B$. Similarly, the components of $B'$ in the same direction of $A$ or $B$.
Thanks in advance,
BK
Generally if you know that for two not collinear vectors $a'=Ra$ and $b'=Rb$ you know also that $R(a \times b)= a' \times b'$ ( $\times$ here vector product and $R$ rotation matrix)
These six vectors are sufficient to construct from them two $3 \times 3$ matrices with vectors as columns, name them $C=[a \ \ b \ \ a\times b]$ and $C'=[a' \ \ b' \ \ a' \times b' ]$.
So we have $C'=RC$.
From this we can calculate rotation matrix $R$.
$R=C'C^{-1}$
$C^{-1}$ exists because $a, b, a\times b$ are not coplanar.