8 files changed, 369 insertions, 113 deletions

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index 5634c4d..4bd6ff4 100644
--- a/mat/domace_naloge/26/dokument.aux
+++ b/mat/domace_naloge/26/dokument.aux
@@ -28,8 +28,8 @@
 \babel@aux{slovene}{}
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 \@writefile{toc}{\contentsline {paragraph}{Navodilo naloge}{1}{section*.1}\protected@file@percent }
-\@writefile{toc}{\contentsline {section}{\numberline {1}Zaključek}{1}{section.1}\protected@file@percent }
 \exsheets@sum@of@points {0}
 \exsheets@sum@of@bonus {0}
 \gdef \numberofquestions {0}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Zaključek}{2}{section.1}\protected@file@percent }
 \gdef \@abspage@last{2}
diff --git a/mat/domace_naloge/26/dokument.log b/mat/domace_naloge/26/dokument.log
index 2f57d85..3aec48b 100644
--- a/mat/domace_naloge/26/dokument.log
+++ b/mat/domace_naloge/26/dokument.log
@@ -1,4 +1,4 @@
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diff --git a/mat/domace_naloge/26/dokument.pdf b/mat/domace_naloge/26/dokument.pdf
index 36f2f01..e422053 100644
--- a/mat/domace_naloge/26/dokument.pdf
+++ b/mat/domace_naloge/26/dokument.pdf
diff --git a/mat/domace_naloge/26/dokument.synctex.gz b/mat/domace_naloge/26/dokument.synctex.gz
index 3c0a2d7..29d69dc 100644
--- a/mat/domace_naloge/26/dokument.synctex.gz
+++ b/mat/domace_naloge/26/dokument.synctex.gz
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
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    **** Error:  An error occurred while reading an XREF table.
    **** The file has been damaged.  This may have been caused
diff --git a/mat/domace_naloge/26/ž b/mat/domace_naloge/26/ž
new file mode 100644
index 0000000..04b062a
--- /dev/null
+++ b/mat/domace_naloge/26/ž
@@ -0,0 +1,211 @@
+% !TeX encoding = UTF-8
+% !TeX spellcheck = sl_SI
+% do-vimlatex-onwrite
+\documentclass[]{article}
+\usepackage[utf8]{inputenc}
+\usepackage{etoolbox}
+\usepackage[hidelinks]{hyperref}
+\usepackage{xurl} % da breaka url
+\usepackage[a4paper, total={7in, 10in}]{geometry}
+\usepackage{graphicx}
+\usepackage{hologo}
+\usepackage{amssymb}
+\usepackage{calculator}
+\usepackage{pgfplots}
+\usepackage[inline]{enumitem}
+\usepackage{siunitx}
+\usepackage{multicol}
+\usepackage{tabularcalc}
+\usepackage{amsmath}
+\usepackage{float}
+\usepackage{tasks}
+\usepackage{filecontents}
+\usepackage{textcomp}
+\usepackage{tkz-euclide}
+\usepackage{dirtytalk}
+\usepackage{csquotes}
+\usepackage{listings}
+\usepackage{datetime} % [ddMMyyyy]
+\usepackage{ccicons}
+\usepackage{chemformula}
+\usepackage{gensymb}
+\usepackage[normalem]{ulem}
+\usepackage[slovene]{babel}
+\usepackage{cancel}
+\usepackage{tabularx}
+\usepackage{xcolor}
+\usepackage{colortbl}
+\usepackage{exsheets}
+\usepackage{harpoon}
+\usepackage{readarray}
+\usepackage{forloop}
+\usepackage[nomessages]{fp}
+\usepackage{multirow}
+\newcolumntype{Y}{>{\centering\arraybackslash}X}
+% \usepackage{multienum} % weird with labels
+\usetikzlibrary{calc} %% not really needed............. idk.
+%\usetikzlibrary{external}
+% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
+%\tikzexternalize
+\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol
+\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}}
+\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development
+\newcommand{\razhroscevanje}{1}
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codered}{rgb}{1,0,0}
+\definecolor{codegray}{rgb}{0.5,0.5,0.5}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
+\renewcommand{\dateseparator}{. }
+\settimeformat{hhmmsstime}
+\lstdefinestyle{mystyle}{
+	backgroundcolor=\color{backcolour},   
+	commentstyle=\color{codegreen},
+	keywordstyle=\color{magenta},
+	numberstyle=\tiny\color{codegray},
+	stringstyle=\color{codepurple},
+	basicstyle=\ttfamily\footnotesize,
+	breakatwhitespace=false,         
+	breaklines=true,                 
+	captionpos=b,                    
+	keepspaces=true,                 
+	numbers=left,                    
+	numbersep=5pt,                  
+	showspaces=false,                
+	showstringspaces=false,
+	showtabs=false,                  
+	tabsize=2
+}
+\lstset{style=mystyle}
+\def\@maketitle{%
+	\newpage
+	\null
+	\vskip 2em%
+	\begin{center}%
+		\let \footnote \thanks
+		{\LARGE \@title \par}%
+		\vskip 1.5em%
+		{\large
+			\lineskip .5em%
+			\begin{tabular}[t]{c}% <------
+				\@author%            <------ Authors
+			\end{tabular}\par}%    <------
+		\vskip 1em%
+		{\large \@date}%
+	\end{center}%
+	\par
+	\vskip 1.5em}
+%opening
+\newcommand{\snovdn}{Skalarni produkt vektorjev }
+\newcommand{\predmdn}{mat}
+\newcommand{\predmkaj}{domace\_naloge}
+\newcommand{\stevilkadn}{26}
+\newcommand{\cm}[1]{\SI{#1}{\centi\meter}}
+\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}}
+\makeatletter
+\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
+\newcommand{\@xslalph}[1]{%
+	\ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i%
+	\or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
+	\or t\or u\or v\or z\or \v{z}
+	\else\@ctrerr\fi%
+}
+\AddEnumerateCounter{\xslalph}{\@xslalph}{m}
+\makeatother
+\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
+\newcommand*\textfrac[2]{
+	\frac{\text{#1}}{\text{#2}}
+}
+\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3)
+\newcommand\vektor{\overrightarrow}
+\newcommand{\iic}{I\textsuperscript{2}C }
+\title{%
+	\snovdn --- \stevilkadn. domača naloga
+	\\
+	\large Matematika, Gimnazija Bežigrad}
+\author{\begin{tabular}{rl}
+		\textbf{Profesor:} & prof. Vilko Domajnko \\
+		\textbf{Avtor:} & Anton Luka Šijanec, 2. a
+%		\textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3
+\end{tabular}}
+\newcommand\hcancel[2][black]{\setbox0=\hbox{$0#2$}%
+\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} 
+% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
+\begin{document}
+\maketitle
+\begin{abstract}
+Ta dokument vsebuje navodila in rešitve domačih nalog snovi \textit{\snovdn}pri matematiki, ki sem jih spisal sam.
+\end{abstract}
+\paragraph{Navodilo naloge} \textbf{vaje2:} 83 / 567, 568, 569
+%\tableofcontents
+\begin{enumerate}[label=\textbf{\arabic*.}]
+	\setcounter{enumi}{566}
+	\item Izračunaj skalarni produkt označenih vektorjev na dva načina (po definiciji in z uporabo pravokotne projekcije enega vektorja na drugi vektor):
+		\begin{tasks}[label=\textbf{\xslalph*)}](2)
+			\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](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}
+			\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}
+			\task v pravilnem 6-kotniku s stranico, dolgo \cm{2},
+			
+				\begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}]
+					\tkzDefPoint(0,0){A} \tkzDefPoint(2,0){B}
+					\tkzDefRegPolygon[name=P,sides=6,side](A,B)
+					\tkzDrawPolygon[fill=red!30, opacity=.3](P1,P2,P3,P4,P5,P6)
+					\tkzDrawSegments[vect](P2,P1 P2,P3)
+				\end{tikzpicture}
+			\task v pravilnem 6-kotniku s stranico, dolgo \cm{2}.
+			
+				\begin{tikzpicture}[vect/.style={->,shorten >=0pt,>=latex'}]
+					\tkzDefPoint(0,0){A} \tkzDefPoint(2,0){B}
+					\tkzDefRegPolygon[name=P,sides=6,side](A,B)
+					\tkzDrawPolygon[fill=red!30, opacity=.3](P1,P2,P3,P4,P5,P6)
+					\tkzDrawSegments[vect](P1,P6 P3,P2)
+				\end{tikzpicture}
+		\end{tasks}
+	\item Kocka $ABCDA'B'C'D'$ ima \cm{10} dolg rob. Izračunaj $\vektor{AB}\cdot\vektor{AC}$, $\vektor{AB}\cdot\vektor{AC'}$,
+		$\vektor{AD'}\cdot\vektor{AC'}$, $\vektor{BD'}\cdot\vektor{DB'}$.
+	\item Tetraeder $ABCD$ ima \cm{10} dolg rob. Izračunaj $\vektor{AB}\cdot\vektor{AC}$, $\vektor{AB}\cdot\vektor{AD}$,
+		$\vektor{AD}\cdot\vektor{AD}$.
+\end{enumerate}
+\section{Zaključek}
+Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
+\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2020}.}
+izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo v mojem šolskem Git repozitoriju na
+\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi 
+\href{https://git.sijanec/sola-gimb-2/src/branch/master/\predmdn/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je  \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}.
+\if\razhroscevanje1
+\vfill
+\section*{Razhroščevalne informacije}
+Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta.
+
+Grafi imajo natančnost \functionSamples\space točk na graf.
+
+Konec generiranja dokumenta: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins"
+
+Dokument se je generiral R0qK1KR2 \SI{}{\second}.
+\fi
+%	\item $$$$ aaasecgeninsaaa R0qK1KR2
+\end{document}