Project ID:
6000000075
Accepted:
Typ:
Layout:
Question:
\begin{minipage}{0.45\linewidth}
Je daný pravidelný šesťuholník $ABCDEF$ so stredom $S$ a dĺžkou strany $1$. V šesťuholníku sú vyznačené vektory $\vec a$, $\vec b$, $\vec c$, $\vec d$ a $\vec e$ (viď obrázok). Vypočítajte skalárne súčiny dvojíc vyznačených vektorov a priraďte im správne výsledky.
\end{minipage}
\hfill
\begin{minipage}{0.45\linewidth}
\obrMsr[x=0.9cm,y=0.9cm]{-4}{4}{-3}4
{
\footnotesize
\coordinate (S) at (0,0);
\coordinate (A) at (240:2);
\coordinate (B) at (300:2);
\coordinate (C) at (0:2);
\coordinate (D) at (60:2);
\coordinate (E) at (120:2);
\coordinate (F) at (180:2);
\fill[vypln1] (A) -- (B) -- (C) -- (D) -- (E) -- (F) -- cycle;
\draw[thick] (A) node [below left]{$A$} -- (B) node [below right]{$B$} -- (C) node [right]{$C$} -- (D) node [above right]{$D$} -- (E) node [above left]{$E$}-- (F) node [left]{$F$} -- cycle;
\draw[green!60!black,-latex,thick] (S) -- node [above,sloped]{$\vec{a}$} (A);
\draw[red,-latex,thick] (S) -- node [above,sloped]{$\vec{b}$} (C);
\draw[blue,-latex,thick] (D) -- node [above,sloped,xshift=-10pt]{$\vec{c}$} (F);
\draw[magenta,-latex,thick] (S) -- node [above,sloped]{$\vec{d}$} (D);
\draw[orange!60!black,-latex,thick] (S) -- node [above,sloped,xshift=-10pt]{$\vec{e}$} (E);
\begin{scope}[thick]
\obrKrizek[2pt]{S}{below right}{S}
\end{scope}
}
\end{minipage}
Questions Title:
Skalárne súčiny:
Answers Title:
Výsledky:
Question 1:
$\vec a\cdot\vec b$
Answer 1:
$-\frac12$
Question 2:
$\vec a\cdot\vec c$
Answer 2:
$\frac32$
Question 3:
$\vec b\cdot\vec d$
Answer 3:
$\frac12$
Question 4:
$\vec c\cdot\vec e$
Answer 4:
$0$
Question 5:
$\vec c\cdot\vec b$
Answer 5:
$-\frac32$
Question 6:
$\vec a\cdot\vec d$
Answer 6:
$-1$
Question 7:
$\vec c\cdot\vec c$
Answer 7:
$3$
Question 8:
$\vec e\cdot\vec e$
Answer 8:
$1$
Tex:
% tiket 33039
\NastavOT{4}
\NastavOD{4}