In Richtung b heißt b:=b/|b| gleiche Länge wie a.
a b = |a| |b| cos(α) ===> α = 153.4277884167°
Rotation um Achse n=(n1,n2,n3) , |n|=1
\(\small R_n(a, n1, n2, n3) \, := \, \left(\begin{array}{rrr}n1^{2} \; \left(1 - \operatorname{cos} \left( a \right) \right) + \operatorname{cos} \left( a \right)&n1 \; n2 \; \left(1 - \operatorname{cos} \left( a \right) \right) - n3 \; \operatorname{sin} \left( a \right)&n1 \; n3 \; \left(1 - \operatorname{cos} \left( a \right) \right) + n2 \; \operatorname{sin} \left( a \right)\\n2 \; n1 \; \left(1 - \operatorname{cos} \left( a \right) \right) + n3 \; \operatorname{sin} \left( a \right)&n2^{2} \; \left(1 - \operatorname{cos} \left( a \right) \right) + \operatorname{cos} \left( a \right)&n2 \; n3 \; \left(1 - \operatorname{cos} \left( a \right) \right) - n1 \; \operatorname{sin} \left( a \right)\\n3 \; n1 \; \left(1 - \operatorname{cos} \left( a \right) \right) - n2 \; \operatorname{sin} \left( a \right)&n3 \; n2 \; \left(1 - \operatorname{cos} \left( a \right) \right) + n1 \; \operatorname{sin} \left( a \right)&n3^{2} \; \left(1 - \operatorname{cos} \left( a \right) \right) + \operatorname{cos} \left( a \right)\\\end{array}\right)\)
R_n(α,n1,n2,n3) a = b
\(\small \left( \begin{array}{rrr}1.89 \; n1 \; n3 + 0.45 \; n2 - 0.01 \\ -0.45 \; n1 + 1.89 \; n2 \; n3 + 0.45 \\ 1.89 \; n3^{2} + 7.11 \cdot 10^{-15} \end{array} \right)=0\)
10^-15 ~ 0 ===> n1,n2,n3
\(R_{ab}=\left(\begin{array}{rrr}1&0.05&0.01\\0.05&-0.89&-0.45\\-0.01&0.45&-0.89\\\end{array}\right)\)
so etwa?
