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r x + s y + t z = 0 ⇔ r ( x 1 x 2 x 3 ) + s ( y 1 y 2 y 3 ) + t ( z 1 z 2 z 3 ) = ( 0 0 0 ) {\displaystyle rx+sy+tz=0\Leftrightarrow r{\begin{pmatrix}x_{1}\\x_{2}\\x_{3}\end{pmatrix}}+s{\begin{pmatrix}y_{1}\\y_{2}\\y_{3}\end{pmatrix}}+t{\begin{pmatrix}z_{1}\\z_{2}\\z_{3}\end{pmatrix}}={\begin{pmatrix}0\\0\\0\end{pmatrix}}}
führt auf
r x 1 + s y 1 + t z 1 = 0 r x 2 + s y 2 + t z 2 = 0 r x 3 + s y 3 + t z 3 = 0 {\displaystyle {\begin{array}{ccccccc}rx_{1}&+&sy_{1}&+&tz_{1}&=&0\\rx_{2}&+&sy_{2}&+&tz_{2}&=&0\\rx_{3}&+&sy_{3}&+&tz_{3}&=&0\\\end{array}}}
