Spurgerade in der $X_{23}$-Ebene ($x_1=0$):
$8+r+5+s+1=0 \Rightarrow s=-8-5r$
Schnittgerade:
$g:x=\left(\begin{array}{r} 8\\[1mm]1\\[1mm]5\\[1mm]\end{array}\right) +r\left(\begin{array}{r} 5\\[1mm]0\\[1mm]1\\[1mm]\end{array}\right) +\left(-8-5r\right)\left(\begin{array}{r} 1\\[1mm]0\\[1mm]2\\[1mm]\end{array}\right) =\left(\begin{array}{r} 0\\[1mm]1\\[1mm]-11\\[1mm]\end{array}\right) +r\left(\begin{array}{r} 0\\[1mm]0\\[1mm]-9\\[1mm]\end{array}\right)$
Spurgerade in der $X_{13}$-Ebene ($x_2=0$):
$1+r+0+s+0=0 \Rightarrow 1=0$ E ist parallel zur $X_{13}$-Ebene.
Spurgerade in der $X_{12}$-Ebene ($x_3=0$):
$5+r+1+s+2=0 \Rightarrow s=-\frac{5}{2}-\frac{1}{2}r$
Schnittgerade:
$g:x=\left(\begin{array}{r} 8\\[1mm]1\\[1mm]5\\[1mm]\end{array}\right) +r\left(\begin{array}{r} 5\\[1mm]0\\[1mm]1\\[1mm]\end{array}\right) +\left(-\frac{5}{2}-\frac{1}{2}r\right)\left(\begin{array}{r} 1\\[1mm]0\\[1mm]2\\[1mm]\end{array}\right) =\left(\begin{array}{r} \frac{11}{2}\\[1mm]1\\[1mm]0\\[1mm]\end{array}\right) +r\left(\begin{array}{r} \frac{9}{2}\\[1mm]0\\[1mm]0\\[1mm]\end{array}\right)$