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+% !TeX encoding = UTF-8
+% !TeX spellcheck = sl_SI
+% do-vimlatex-onwrite
+\documentclass[]{article}
+\usepackage[utf8]{inputenc}
+\usepackage{etoolbox}
+\usepackage[hidelinks]{hyperref}
+\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}
+\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}{Množenje vektorja s številom }
+\newcommand{\predmdn}{mat}
+\newcommand{\predmkaj}{domace\_naloge}
+\newcommand{\stevilkadn}{20}
+\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{$#2$}%
+\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 domačo nalogo, ki zajema snov \textit{\snovdn}pri matematiki, in njene rešitve, ki sem jih spisal sam. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbral naključno.
+\end{abstract}
+\tableofcontents
+\section{Vaje \textit{Matematika 2}: stran 50, dve sodi in dve lihi nalogi 317-336}
+\begin{enumerate}[label=\textbf{\arabic*.}] % 318, 329, 320, 325
+	\if\false1
+		\setcounter{enumi}{317}
+		\item Nariši vektor $\vektor{a}$, dolg \cm{3}. Nariši še vektorje:
+			\footnote{Za sezname ne uporabljam več \texttt{enumerate}, ampak \texttt{tasks} (Deutsche Kvalität)}
+			\begin{primerTasks}(8)
+				\task $\displaystyle\frac{1}{3}\Vec{a}$ % a
+				\task $\displaystyle\frac{4}{5}\Vec{a}$ % b
+				\task $\displaystyle-\frac{3}{7}\Vec{a}$ % c
+				\task $\displaystyle-\frac{3}{4}\Vec{a}$ % č
+				\task $\displaystyle\frac{5}{4}\Vec{a}$ % d
+				\task $\displaystyle\frac{7}{5}\Vec{a}$ % e
+				\task $\displaystyle-\frac{3}{2}\Vec{a}$ % f
+				\task $\displaystyle-\frac{8}{5}\Vec{a}$ % g
+				\task $\displaystyle\sqrt{2}\Vec{a}$ % h
+				\task $\displaystyle\sqrt{5}\Vec{a}$ % i
+				\task $\displaystyle-\sqrt{7}\Vec{a}$ % j
+				\task $\displaystyle-\sqrt{10}\Vec{a}$ % k
+				\task $\displaystyle\frac{\sqrt{3}}{4}\Vec{a}$ % l
+				\task $\displaystyle\frac{\sqrt{6}}{7}\Vec{a}$ % m
+				\task $\displaystyle-\frac{\sqrt{12}}{3}\Vec{a}$ % n
+				\task $\displaystyle-\frac{\sqrt{15}}{8}\Vec{a}$ % o
+			\end{primerTasks}
+			\begin{center}
+				\begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}]
+					% 0	
+					\tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B}
+					\tkzDrawPoints[red](A,B) \tkzDrawSegments[vect](A,B)
+					\tkzLabelLine[above](A,B){$\Vec{a}$}
+					% a
+					\tkzDefPoint(30:3){aA}
+					\tkzDrawLine(A,aA) \tkzDrawLine(aA,B)
+					\tkzDefPoint(1,0){a1} \tkzDefPoint(30:1){a2} \tkzDefPoint(30:2){a3}
+					\tkzDefPoint(2,0){a4}
+					\tkzCompass(A,a2) \tkzCompass(a2,a3) \tkzDrawLine(a3,a4)
+					\tkzDrawLine(a1,a2) \tkzDrawPoints[red](a1) \tkzDrawSegment[vect](A,a1)
+					\tkzLabelLine[below](A,a1){$\frac{1}{3}\Vec{a}$}
+					% b
+					\tkzDefPoint(30:(3/5)){b1} \tkzDefPoint(30:(3/5)*2){b2}
+					\tkzDefPoint(30:(3/5)*3){b3} \tkzDefPoint(30:(3/5)*4){b4}
+					\tkzCompass(A,b1) \tkzCompass(b1,b2) \tkzCompass(b2,b3)
+					\tkzCompass(b3,b4) \tkzCompass(b4,aA)
+					\tkzDefPoint((3/5)*4,0){b5} \tkzDrawLine(b4,b5) \tkzDrawPoints[red](b5)
+					\tkzDrawSegments[vect](A,b5)
+					\tkzLabelLine[below](A,b5){$\frac{4}{5}\Vec{a}$}
+				\end{tikzpicture}
+			\end{center}
+		\fi
+	\setcounter{enumi}{318}
+	\item Nariši trikotnik $ABC$ s podatki $a=\cm{4}$, $b=\cm{6}$, $c=\cm{7}$. Nariši še $\displaystyle\frac{1}{3}\vektor{AC}+\sqrt{2}\vektor{AB}$. % 319
+		\begin{center}
+			\begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}]
+				\tkzDefPoint(0,0){A} \tkzDefPoint(7,0){B}
+				\tkzDefPoint(6,0){bh} \tkzDefPoint(7-4,0){ah}
+				\tkzDefPoint(0,6){3h} \tkzDefPoint(0,4){2h} \tkzDefPoint(0,2){1h}
+				\tkzCompass(A,B) \tkzDrawLine(A,B) % \tkzLabelLine[below](A,B){$c$}
+				\tkzInterCC(A,bh)(B,ah) \tkzGetPoints{C}{CX}
+				\tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C)
+				\tkzLabelLine[below right](A,C){$\vektor{AC}$}
+				\tkzDrawLine(A,3h) \tkzCompass(A,1h) \tkzCompass(1h,2h)
+				\tkzCompass(2h,3h) \tkzDrawLine(3h,C)
+				\tkzDefPointWith[colinear=at 1h](3h,C) \tkzGetPoint{Z}
+				\tkzInterLL(A,C)(1h,Z) \tkzGetPoint{T}
+				\tkzLabelLine[above](A,T){$\frac{1}{3}\vektor{AC}$}
+				% sedaj pa sqrt(2)AB
+				\tkzDefPoint(0,7){P} \tkzCompass(A,P)
+				\tkzDefPoint(7,7){K} \tkzDrawLine(B,K) \tkzDrawLine(P,K)
+				\tkzInterLC(A,B)(A,K) \tkzGetPoints{K2X}{K2} \tkzCompass(A,K2)
+				\tkzLabelLine[below](A,K2){$\sqrt{2}\vektor{AB}$}
+				% sedaj pa seštevek
+				\tkzDefPointWith[colinear=at B](A,C) \tkzGetPoint{S}
+				\tkzLabelLine[above left](A,S){$\frac{1}{3}\vektor{AC}+\sqrt{AB}$}
+				\tkzDrawSegments[vect](A,C A,T, A,K A,K2)
+				\tkzDrawSegments[red, vect](A,S)
+				\tkzMarkRightAngles(A,P,K P,K,B K,B,A B,A,P)
+				\tkzDrawPoints[red](A,B,C,T,K,K2,S) \tkzLabelPoints(A,B,C)
+			\end{tikzpicture}
+		\end{center}
+	\newpage
+	\item Nariši pravokotnik $ABCD$ s podatki: $a=\cm{6}$, $b=\cm{2}$. Nariši še $\displaystyle-\frac{3}{2}\vektor{AC}+\frac{\sqrt{2}}{2}\vektor{BC}$.
+		\begin{center}
+			\begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}]
+				\tkzDefPoint(0,0){A} \tkzDefPoint(6,2){C} \tkzDefPoint(6,0){B}
+				\tkzDefPoint(0,2){D}
+				\tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C,D)
+				\tkzDefPoint(0,(2/3)){a1} \tkzDefPoint(0,(2/3)*2){a2}
+				\tkzCompass(A,a1) \tkzCompass(a1,a2) \tkzCompass(a2,D)
+				\tkzDefPointWith[colinear=at a1](D,C) \tkzGetPoint{Z}
+				\tkzInterLL(A,C)(a1,Z) \tkzGetPoint{V}
+				\tkzDrawLine(a1,V) \tkzLabelLine[above left](A,C){$\vektor{AC}$}
+				\tkzLabelLine[below](V,C){$-\frac{2}{3}\vektor{AC}$}
+				% zdaj pa še koren iz dve polovic vektorja BC
+				\tkzDefPoint(6-2,0){K} \tkzDefPoint(6-2,2){P}
+				\tkzCompass(B,K) \tkzCompass(C,P)
+				\tkzInterLC(C,B)(C,K) \tkzGetPoints{K2X}{K2}
+				\tkzDefMidPoint(C,K2) \tkzGetPoint{K22}
+				\tkzLabelLine[left](C,K22){$\frac{\sqrt{2}}{2}\vektor{CB}$}
+				\tkzDefPointWith[colinear=at K22](C,V) \tkzGetPoint{S}
+				\tkzDrawPoints[red](A,B,C,D,V,K2,K22,S) \tkzLabelPoints[](A,B,C,D)
+				\tkzDrawSegments[vect](A,C C,V C,K2 C,K22)
+				\tkzDrawSegments[vect, red](C,S)
+				\tkzMarkRightAngles(C,P,K P,K,B K,B,C B,C,P)
+			\end{tikzpicture}
+		\end{center}
+	\setcounter{enumi}{324}
+	\item Naj bo $\Vec{m}=2\Vec{a}+3\Vec{b}$ in $\Vec{n}=\Vec{a}-2\Vec{b}$. Izrazi vektor $2\Vec{m}-\frac{1}{2}\Vec{n}$ z vektorjema $\Vec{a}$ in $\Vec{b}$.
+		$$
+			2\Vec{a}+3\Vec{b}-(\frac{1}{2}(\Vec{a}-2\Vec{b})) = 
+			2\Vec{a} + 3\Vec{b} - \frac{1}{2}\Vec{a} + \frac{1}{2} \cdot 2\Vec{b} =
+			1\frac{1}{2}\Vec{a}+4\Vec{b}
+		$$
+	\setcounter{enumi}{328}
+	\item Nariši daljico $AB$, dolgo \cm{6}. Na njen nariši tako točno $M$, da velja $|AM|:|MB|=1:2$, in tako točno $N$, da velja $|AN|:|AB|=1:2$. Vektorja $\vektor{AM}$ in $\vektor{AN}$ izrazi z vektorjem $\vektor{AB}$.
+		\begin{center}
+			\begin{tikzpicture}[vect/.style={->,shorten >=3pt,>=latex'}]
+				\tkzDefPoint(0,0){A} \tkzDefPoint(6,0){B}
+				\tkzCompass(A,B) \tkzDrawLine(A,B) % \tkzLabelLine[below](A,B){$AB$}
+				\tkzDefPoint(30:6){3h} \tkzDefPoint(30:4){2h} \tkzDefPoint(30:2){1h}
+				\tkzDrawLine(A,3h) \tkzDrawLine(3h,B)
+				\tkzCompass(A,1h) \tkzCompass(1h,2h) \tkzCompass(2h,3h)
+				\tkzDefPoint((6/3)*1,0){M} \tkzDrawLine(h1,M)
+				\tkzDefMidPoint(A,B) \tkzGetPoint{N}
+				\tkzDrawPoints[red](A,B,M,N) \tkzLabelPoints[below left](A,B,M,N)
+				\tkzDrawSegments[vect](A,M A,N)
+			\end{tikzpicture}
+		\end{center}
+		$$
+			\vektor{AM} = \frac{1}{3}\vektor{AB}
+		$$
+		$$
+			\vektor{AN} = \frac{1}{2}\vektor{AB}
+		$$
+\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
+\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}