Two pairs of mutually orthogonal 3-dimensional vectors of unit length are given: $(n_1,n_2)$ and $(m_1,m_2)$:
$n_1 \cdot n_2 = 0$
$m_1 \cdot m_2 = 0$
Obviously, rotation exists that, when applied to $(m_1,m_2)$, makes $m_1$ parallel to $n_1$ and $m_2$ parallel to $n_2$.
Is it possible to express this rotation vector through $n_1,n_2,m_1,m_2$ using only the following operations:
- summation/subtraction
- multiplication by a scalar
- scalar multiplication of vectors
- vector multiplication of vectors
?