1003233605
Časť:
C
Dané sú mimobežné priamky $p$ a $q$.
\begin{align*}
p\colon x&= 1-t, & q\colon x&= 1-2s, \\
y&= 1+t, & y&=s, \\
z&= 3+2t;\ t\in\mathbb{R}, & z&= 3+3s;\ s\in\mathbb{R}.
\end{align*}
Nájdite parametrické vyjadrenie priamky r, ktorá pretína obe priamky $p$ a $q$ a leží v rovine $x+2y-z+2=0$.
$\begin{aligned}
r\colon x&=-1+2m, \\
y&=3-3m, \\
z&=7-4m;\ m\in\mathbb{R}
\end{aligned}$
$\begin{aligned}
r\colon x&=-1+m, \\
y&=3+3m, \\
z&=7-m;\ m\in\mathbb{R}
\end{aligned}$
$\begin{aligned}
r\colon x&=-1+3m, \\
y&=3+2m, \\
z&=7+5m;\ m\in\mathbb{R}
\end{aligned}$
$\begin{aligned}
r\colon x&=-1+m, \\
y&=3-m, \\
z&=7+m;\ m\in\mathbb{R}
\end{aligned}$
