9000117401
Część:
B
Określ część wspólną przecięcia płaszczyzn \(\rho \)
i \(\sigma \).
\[\begin{aligned}
\rho \colon 2x - 5y + 4z - 10 = 0,\qquad \sigma \colon x - y - z - 2 = 0 & &
\end{aligned}\]
\(\begin{aligned}[t] p\colon x& = 3t, &
\\y & = -2 + 2t,
\\z & = t;\ t\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] q\colon x& = 2s - 10,&
\\y & = 5s - 10,
\\z & = s;\ s\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] a\colon x& = 2u - 4,&
\\y & = 2u - 4,
\\z & = u;\ u\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] b\colon x& = 3v + 1,&
\\y & = v - 2,
\\z & = v;\ v\in \mathbb{R}
\\ \end{aligned}\)