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Rovnica priamky ako priesečnica rovín
Urči rovnicu priamky, ktorá je priesečnicou zadaných rovín:
\( \begin{array}{rlrl} \pi: x & =1-t+s & \rho: x & =3+r+p \\ y & =4 t+s & y & =3-r+p \\ z & =2 t+s & z & =3+r-2 p \end{array} \)
\( \large\begin{array}{l}x=\frac83+\frac72p\\ y=\frac{10}{3}-\frac32p\\ z=\frac83+\frac12p;p\in\mathbb{R}\end{array} \)
\( \large\begin{array}{l}x=\frac83+\frac72p\\ y=\frac{10}{3}+\frac32p\\ z=\frac83-\frac12p;p\in\mathbb{R}\end{array} \)
\( \large\begin{array}{l}x=\frac83-\frac72p\\ y=\frac{10}{3}+\frac32p\\ z=\frac83-\frac12p;p\in\mathbb{R}\end{array} \)
\( \large\begin{array}{l}x=\frac83+\frac72p\\ y=\frac{10}{3}-\frac32p\\ z=\frac83-\frac32p;p\in\mathbb{R}\end{array} \)