回復 1# thankyou 的帖子
\({{L}_{1}}:\left\{ \begin{align}
& x=1+t \\
& y=1 \\
& z=t \\
\end{align} \right.\quad {{L}_{2}}:\left\{ \begin{align}
& x=1 \\
& y=1+2s \\
& z=1+s \\
\end{align} \right.\quad \)
設\({{L}_{3}}\)和\({{L}_{1}}\)交於\(P\left( 1+t,1,t \right)\)，\({{L}_{3}}\)和\({{L}_{2}}\)交於\(Q\left( 1,1+2s,1+s \right)\)
由於\(E,P,Q\)共線
\(\begin{align}
& \frac{1+t-2}{1-2}=\frac{1-0}{1+2s-0}=\frac{t-1}{1+s-1} \\
& s=-1 \\
& Q=\left( 1,-1,0 \right) \\
& {{L}_{3}}:\frac{x-2}{1}=\frac{y}{1}=\frac{z-1}{1} \\
\end{align}\)
