Project ID:
6000000039
Accepted:
Typ:
Layout:
Question:
Přímka $p$ je dána bodem $A$ a normálovým vektorem $\vec{n}$ (viz obrázek). Vyberte její obecnou rovnici.
Answers Title:
\vspace{20pt}
Question 1:
{\obrA}
Question 1 Image:
Answer 1:
$2x-5y-6=0$
Question 2:
{\obrB}
Question 2 Image:
Answer 2:
$x-5y-3=0$
Question 3:
{\obrC}
Question 3 Image:
Answer 3:
$5x-y-15=0$
Question 4:
{\obrD}
Question 4 Image:
Answer 4:
$5x+y-15=0$
Question 5:
{\obrE}
Question 5 Image:
Answer 5:
$5x-2y-15=0$
Question 6:
{\obrF}
Question 6 Image:
Answer 6:
$2x+5y-6=0$
Answer 7:
$2x-5y+6=0$
Answer 8:
$x+5y-3=0$
Tex:
% tiket 32337
\NastavOD{2}
\usetikzlibrary{arrows,decorations.markings}
\def\obrA{\obrMsr[x=0.45cm,y=0.45cm]{-5}{10}{-3}6
{
\footnotesize
\coordinate (A) at (3,0);
\coordinate (B) at (1,5);
\obrClip
\draw[gray!20,thin, step=1] (-5,-3) grid (10,6);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-4,-2,2,4,6,8}
\obrPopisY[left]{2,4}
\obrFce{(2*(\x)-6)/5}
\draw[thick,green!60!black,,decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=stealth]{latex}}},postaction={decorate}] (3,0) -- node [above right]{$\vec{n}$} (1,5);
\draw[blue] (3,-1) node[yshift=-2pt]{$A=[3;0]$};
\draw[red] (8,2) node[above left]{$p$};
\begin{scope}[thick,blue]
\obrKrizek[2pt]{A}{}{}
\obrKrizek[2pt]{B}{}{}
\end{scope}
}}
\def\obrB{\obrMsr[x=0.45cm,y=0.45cm]{-3}{10}{-6}3
{
\footnotesize
\coordinate (A) at (3,0);
\coordinate (B) at (4,-5);
\obrClip
\draw[gray!20,thin, step=1] (-3,-6) grid (10,3);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2,4,6,8}
\obrPopisY[left]{-4,-2,2}
\obrFce{((\x)-3)/5}
\draw[thick,green!60!black,,decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=stealth]{latex}}},postaction={decorate}] (3,0) -- node [above right]{$\vec{n}$} (4,-5);
\draw[blue] (3,1) node[yshift=-4pt]{$A=[3;0]$};
\draw[red] (8,1) node[above left]{$p$};
\begin{scope}[thick,blue]
\obrKrizek[2pt]{A}{}{}
\obrKrizek[2pt]{B}{}{}
\end{scope}
}}
\def\obrC{\obrMsr[x=0.45cm,y=0.45cm]{-3}{10}{-5}5
{
\footnotesize
\coordinate (A) at (3,0);
\coordinate (B) at (8,-1);
\obrClip
\draw[gray!20,thin, step=1] (-3,-5) grid (10,5);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2,4,6,8}
\obrPopisY[left]{-4,-2,2,4}
\obrFce{(5*(\x)-15)}
\draw[thick,green!60!black,,decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=stealth]{latex}}},postaction={decorate}] (3,0) -- node [below left]{$\vec{n}$} (8,-1);
\draw[blue] (3,1) node[right, yshift=-6pt]{$A=[3;0]$};
\draw[red] (4,3) node[]{$p$};
\begin{scope}[thick,blue]
\obrKrizek[2pt]{A}{}{}
\obrKrizek[2pt]{B}{}{}
\end{scope}
}
}
\def\obrD{\obrMsr[x=0.45cm,y=0.45cm]{-3}{10}{-5}5
{
\footnotesize
\coordinate (A) at (3,0);
\coordinate (B) at (8,1);
\obrClip
\draw[gray!20,thin, step=1] (-3,-5) grid (10,5);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2,4,6,8}
\obrPopisY[left]{-4,-2,2,4}
\obrFce{(5*(\x)-15)}
\draw[thick,green!60!black,,decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=stealth]{latex}}},postaction={decorate}] (3,0) -- node [above left]{$\vec{n}$} (8,1);
\draw[blue] (3,1) node[left,yshift=-6pt]{$A=[3;0]$};
\draw[red] (3,3) node[]{$p$};
\begin{scope}[thick,blue]
\obrKrizek[2pt]{A}{}{}
\obrKrizek[2pt]{B}{}{}
\end{scope}
}}
\def\obrE{\obrMsr[x=0.45cm,y=0.45cm]{-3}{10}{-5}5
{
\footnotesize
\coordinate (A) at (3,0);
\coordinate (B) at (8,-2);
\obrClip
\draw[gray!20,thin, step=1] (-3,-5) grid (10,5);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2,4,6,8}
\obrPopisY[left]{-4,-2,2,4}
\obrFce{(5*(\x)-15)/2}
\draw[thick,green!60!black,,decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=stealth]{latex}}},postaction={decorate}] (3,0) -- node [below left]{$\vec{n}$} (8,-2);
\draw[blue] (3,1) node[left,yshift=-6pt]{$A=[3;0]$};
\draw[red] (4,4) node[]{$p$};
\begin{scope}[thick,blue]
\obrKrizek[2pt]{A}{}{}
\obrKrizek[2pt]{B}{}{}
\end{scope}
}}
\def\obrF{\obrMsr[x=0.45cm,y=0.45cm]{-3}{10}{-6}4
{
\footnotesize
\coordinate (A) at (3,0);
\coordinate (B) at (1,-5);
\obrClip
\draw[gray!20,thin, step=1] (-3,-6) grid (10,4);
\obrOsaX[above left]
\obrOsaY[below right]
\obrPopisX[below]{-2,2,4,6,8}
\obrPopisY[left]{-4,-2,2}
\obrFce{(-2*(\x)+6)/5}
\draw[thick,green!60!black,,decoration={markings,mark=at position 1 with
{\arrow[scale=2,>=stealth]{latex}}},postaction={decorate}] (3,0) -- node [above left]{$\vec{n}$} (1,-5);
\draw[blue] (3,1) node[right,yshift=-6pt]{$A=[3;0]$};
\draw[red] (9,-2) node[]{$p$};
\begin{scope}[thick,blue]
\obrKrizek[2pt]{A}{}{}
\obrKrizek[2pt]{B}{}{}
\end{scope}
}}