MPQ = (1|-1|0) ; MRS = (-1|1|0) ; Verbindungsgerade g: \(\vec{x}\) = \(\begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}\) + r • \(\begin{pmatrix} -1 \\ 1 \\ 0 \end{pmatrix}\)
MPR = (-1|-1|0) ; MQS = (1|1|0) ; Verbindungsgerade h: \(\vec{x}\) = \(\begin{pmatrix} -1 \\ -1 \\ 0 \end{pmatrix}\) + s • \(\begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}\)
\(\begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}\) • \(\begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}\) = 0
→ g ⊥ h
Schnittmenge von g und h:
\(\begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}\) + r • \(\begin{pmatrix} -1 \\ 1 \\ 0 \end{pmatrix}\) = \(\begin{pmatrix} -1 \\ -1 \\ 0 \end{pmatrix}\) + s • \(\begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}\)
1 - r = -1 + s → s = 2 - r
-1 + r = -1 + s → s = r → s = r = 1
Schnittpunkt S(0|0|0)
Gruß Wolfgang