Für \(R(r_x|x_y|r_z)\) muss gelten:

I: \(\left | \overrightarrow{PR} \right | = 5 \sqrt{2} \Leftrightarrow \left | \begin{pmatrix} r_x+3 \\r_y -2 \\ r_z-9\end{pmatrix} \right | = 5 \sqrt{2} \Leftrightarrow \sqrt{(r_x+3)^2 + (r_y-2)^2 + (r_z-9)^2} = 5\sqrt{2}\)

II: \(0.5 = \dfrac{\overrightarrow{PR} \circ \overrightarrow{PQ}}{\left | \overrightarrow{PR}\right | \cdot \left |\overrightarrow{PQ}\right |} \Leftrightarrow  \dfrac{1}{\sqrt{2}} = \dfrac{r_x-r_z+12}{\sqrt{(-r_x - 3)^2 +(2 - r_y)^2 +(9 - r_z)^2}}\)

III: \(r_x-r_y= -10\)