a) A(5/4/3) B(7/7/5)
E:2x+3y+3z=12
\(g_{AB}: \vec{x} = \begin{pmatrix} 5\\4\\3 \end{pmatrix} + r \left( \begin{pmatrix} 7 \\ 7 \\ 5 \end{pmatrix} - \begin{pmatrix} 5\\4\\3 \end{pmatrix} \right)\)
\(g_{AB}: \vec{x} = \begin{pmatrix} 5\\4\\3 \end{pmatrix} + r \begin{pmatrix} 2\\3\\2 \end{pmatrix} \)
\(g_{AB}: \vec{x} = \begin{pmatrix} 5+2r\\4+3r\\3+2r \end{pmatrix} \)
\(E:2x+3y+3z=12\)
g in E einsetzen:
\(2\cdot(5+2r) + 3\cdot(4+3r) + 3 \cdot(3+2r) =12\)
\(10+4r+12+9r+9+6r=12\)
\(31+19r=12\)
\(r=-1\)
\(\vec{x_S} = \begin{pmatrix} 5-2\\4-3\\3-2 \end{pmatrix} = \begin{pmatrix} 3\\ 1\\1 \end{pmatrix} \)
b) ... S(2|3|2)
