i need a little help. Did someone have an idea how to prove this?
Thanks in advance.
Be $\Phi$ an direct isometry of the euclidean Space $\mathbb{R}^3$ with
$\Phi (\left(\begin{eqnarray} 2\\0 \\1 \end{eqnarray}\right))$=$\left(\begin{eqnarray} 2\\1 \\0 \end{eqnarray}\right)$ and $\Phi (\left(\begin{eqnarray} 1\\1 \\0 \end{eqnarray}\right)) $=$ \frac{1}{3} \left(\begin{eqnarray} 1\\4 \\1 \end{eqnarray}\right)$
Why is $\Phi$ a rotation?