Časť:
Project ID:
2010008908
Source Problem:
Accepted:
0
Clonable:
1
Easy:
0
Dané sú mimobežné priamky $a$ a $b$.
\begin{align*}
a\colon x&= -1-2t, & b\colon x&= 1-3s, \\
y&= -2+3t, & y&=2s, \\
z&= -4+2t;\ t\in\mathbb{R}, & z&= 2-2s;\ s\in\mathbb{R}.
\end{align*}
Nájdite parametrické vyjadrenie priamky $p$, ktorá pretína obe priamky $a$ a $b$ a leží v rovine $2x+3y-z-8=0$.
$\begin{aligned}
p\colon x&=-9+r, \\
y&=10+r, \\
z&=4+5r;\ r\in\mathbb{R}
\end{aligned}$
$\begin{aligned}
p\colon x&=-9-2r, \\
y&=10-2r, \\
z&=4+10r;\ r\in\mathbb{R}
\end{aligned}$
$\begin{aligned}
p\colon x&=-9-10r, \\
y&=10+9r, \\
z&=4-r;\ r\in\mathbb{R}
\end{aligned}$
$\begin{aligned}
p\colon x&=-9+2r, \\
y&=10+2r, \\
z&=4-2r;\ r\in\mathbb{R}
\end{aligned}$