1 files changed, 14 insertions, 0 deletions

diff --git a/mat/domace_naloge/26/dokument.tex b/mat/domace_naloge/26/dokument.tex
index 2871afb..691a83e 100644
--- a/mat/domace_naloge/26/dokument.tex
+++ b/mat/domace_naloge/26/dokument.tex
@@ -148,24 +148,28 @@ Ta dokument vsebuje navodila in rešitve domačih nalog snovi \textit{\snovdn}pr
 					\tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C)
 					\tkzDrawSegments[vect](A,B A,C)
 				\end{tikzpicture}
+				$$\Vec{c}\cdot\Vec{b}=|\Vec{c}|\cdot|\Vec{b}|=9\cdot\cos{\ang{60}}=4,5$$
 			\task v enakostraničnem trikotniku s stranico, dolgo \cm{3},
 				\begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}]
 					\tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B} \tkzDefPoint(60:3){C}
 					\tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C)
 					\tkzDrawSegments[vect](C,A B,C)
 				\end{tikzpicture}
+				$$\Vec{a}\cdot\Vec{b}=|\Vec{a}|\cdot|\Vec{b}|\cdot\cos{\left(\ang{180}-\ang{60}\right)}=-4,5$$
 			\task v pravokotniku s stranicama, dolgima \cm{6} in \cm{2},
 				\begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}]
 					\tkzDefPoint(0,0){A} \tkzDefPoint(6,0){B} \tkzDefPoint(6,2){C} \tkzDefPoint(0,2){D}
 					\tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C,D)
 					\tkzDrawSegments[vect](A,B B,C)
 				\end{tikzpicture}
+				$$\Vec{a}\cdot\Vec{b}=|\Vec{a}|\cdot|\Vec{b}|\cdot\cos{\ang{90}}=0$$
 			\task v pravokotniku s stranicama, dolgina \cm{6} in \cm{2},
 				\begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}]
 					\tkzDefPoint(0,0){A} \tkzDefPoint(6,0){B} \tkzDefPoint(6,2){C} \tkzDefPoint(0,2){D}
 					\tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C,D)
 					\tkzDrawSegments[vect](A,B A,C)
 				\end{tikzpicture}
+				$$\vektor{b}\cdot\vektor{e}=|\vektor{b}|\cdot|\vektor{e}|\cdot\cos{\left(\sqrt{\cm{6}^2+\cm{2}^2}\right)}\Dot=11,926966$$
 			\task v pravilnem 6-kotniku s stranico, dolgo \cm{2},
 			
 				\begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}]
@@ -174,6 +178,7 @@ Ta dokument vsebuje navodila in rešitve domačih nalog snovi \textit{\snovdn}pr
 					\tkzDrawPolygon[fill=red!30, opacity=.3](P1,P2,P3,P4,P5,P6)
 					\tkzDrawSegments[vect](P2,P1 P2,P3)
 				\end{tikzpicture}
+				$$\vektor{P_1P_2}\cdot\vektor{P_2P_3}=|\vektor{P_1P_2}|\cdot|\vektor{P_2P_3}|\cdot\cos{\ang{120}}=-2$$
 			\task v pravilnem 6-kotniku s stranico, dolgo \cm{2}.
 			
 				\begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}]
@@ -182,11 +187,20 @@ Ta dokument vsebuje navodila in rešitve domačih nalog snovi \textit{\snovdn}pr
 					\tkzDrawPolygon[fill=red!30, opacity=.3](P1,P2,P3,P4,P5,P6)
 					\tkzDrawSegments[vect](P1,P6 P3,P2)
 				\end{tikzpicture}
+				$$\Vec{P_6P_1}\cdot\Vec{P_3P_2}=|\Vec{P_6P_1}|\cdot|\Vec{P_3P_2}|\cdot\cos{\ang{120}}=-2$$
 		\end{tasks}
 	\item Kocka $ABCDA'B'C'D'$ ima \cm{10} dolg rob. Izračunaj $\vektor{AB}\cdot\vektor{AC}$, $\vektor{AB}\cdot\vektor{AC'}$,
 		$\vektor{AD'}\cdot\vektor{AC'}$, $\vektor{BD'}\cdot\vektor{DB'}$.
+		$$\vektor{AB}\cdot\vektor{AC}=\cm{10}\cdot\cm{10}\cdot\cos{\ang{45}}=50$$
+		$$\vektor{AB}\cdot\vektor{AC'}=\cm{10}\cdot\sqrt{\cm{10}^2+\cm{10}^2}\cdot\cos{\ang{45}}=70,710678$$
+		$$\vektor{AD'}\cdot\vektor{AC'}=\cm{10}\cdot\sqrt{\cm{10}^2+\cm{10}^2}\cdot\cos{\ang{45}}=100$$
+		$$\vektor{BD'}\cdot\vektor{DB'}=\sqrt{\cm{10}^2+\cm{10}^2}\cdot\sqrt{\cm{10}^2+\cm{10}^2}\cos\ang{45}=100$$
 	\item Tetraeder $ABCD$ ima \cm{10} dolg rob. Izračunaj $\vektor{AB}\cdot\vektor{AC}$, $\vektor{AB}\cdot\vektor{AD}$,
 		$\vektor{AD}\cdot\vektor{AD}$.
+		\def\kot{70,528779}
+		$$\vektor{AB}\cdot\vektor{AC}=\cm{10}\cdot\cm{10}\cdot\cos\arccos\frac{1}{3}=33,\overline{3}$$
+		$$\vektor{AB}\cdot\vektor{AD}=\cm{10}\cdot\cm{10}\cdot\cos\arccos\frac{1}{3}=33,\overline{3}$$
+		$$\vektor{AD}\cdot\vektor{AD}=100$$
 \end{enumerate}
 \section{Zaključek}
 Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in