9000106301
Časť:
B
Rovina \(\alpha \) je daná
všeobecnou rovnicou: \(2x + y - z - 5 = 0\).
Určte parametrické vyjadrenie priamky
\(k\), ktorá je kolmá
na rovinu \(\alpha \) a
prechádza bodom \(A = [0;0;1]\).
\(\begin{aligned}[t] x& =\phantom{ 1 -} 2t, &
\\y& =\phantom{ 1 -}\ t,
\\z& = 1 - t;\ t\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] x& =\phantom{ -}2 + 2m, &
\\y& =\phantom{ -}1 +\phantom{ 2}m,
\\z& = -1 -\phantom{ 2}m;\ m\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] x& =\phantom{ -}2k, &
\\y& =\phantom{ -2}k,
\\z& = -\phantom{2}k;\ k\in \mathbb{R}
\\ \end{aligned}\)
\(\begin{aligned}[t] x& =\phantom{ -}2, &
\\y& =\phantom{ -}1,
\\z& = -1 + u;\ u\in \mathbb{R}
\\ \end{aligned}\)
