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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 (\begin{pmatrix} 2\\0 \\1 \end{pmatrix})##=##\begin{pmatrix} 2\\1 \\0 \end{pmatrix}## and ##\Phi (\begin{pmatrix} 1\\1 \\0 \end{pmatrix}) ##=## \frac{1}{3} \begin{pmatrix} 1\\4 \\1 \end{pmatrix}##

Why is ##\Phi## a rotation?

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# I Why is this Isometry a rotation?

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