$P(1\mathrm{\mid }\mathrm{1,5});Q(3\mathrm{\mid }\mathrm{0,5})P(1|1\{,\}5);\backslash ;Q(3|0\{,\}5)$ und $R(5\mathrm{\mid }3)R(5|3)$

$\overrightarrow{PQ}=\vec{Q}-\vec{P}=\left(\begin{array}{c}3\\ \mathrm{0,5}\end{array}\right)-\left(\begin{array}{c}1\\ \mathrm{1,5}\end{array}\right)=\left(\begin{array}{c}2\\ -1\end{array}\right)\backslash overrightarrow\{PQ\}=\backslash vec\; Q-\backslash vec\; P=\backslash begin\{pmatrix\}3\backslash \backslash 0\{,\}5\backslash end\{pmatrix\}-\backslash begin\{pmatrix\}1\backslash \backslash 1\{,\}5\backslash end\{pmatrix\}=\backslash begin\{pmatrix\}2\backslash \backslash -1\backslash end\{pmatrix\}$

$\overrightarrow{PR}=\vec{R}-\vec{P}=\left(\begin{array}{c}5\\ 3\end{array}\right)-\left(\begin{array}{c}1\\ \mathrm{1,5}\end{array}\right)=\left(\begin{array}{c}4\\ \mathrm{1,5}\end{array}\right)\backslash overrightarrow\{PR\}=\backslash vec\; R-\backslash vec\; P=\backslash begin\{pmatrix\}5\backslash \backslash 3\backslash end\{pmatrix\}-\backslash begin\{pmatrix\}1\backslash \backslash 1\{,\}5\backslash end\{pmatrix\}=\backslash begin\{pmatrix\}4\backslash \backslash 1\{,\}5\backslash end\{pmatrix\}$

$A_{Dreieck}=\frac{1}{2}\mathrm{\mid }\overrightarrow{PQ}\times \overrightarrow{PR}\mathrm{\mid }A\_\{Dreieck\}=\backslash frac\{1\}\{2\}|\backslash overrightarrow\{PQ\}\backslash times\backslash overrightarrow\{PR\}|$

FE