From 3b2531de024af4ba031b81282c36bd1bdce7aa02 Mon Sep 17 00:00:00 2001 From: sijanec Date: Sun, 21 Feb 2021 21:04:32 +0100 Subject: =?UTF-8?q?re=C5=A1itve=20skalarni=20produkt=20vektorjev?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- mat/domace_naloge/26/dokument.aux | 2 +- mat/domace_naloge/26/dokument.log | 71 ++++++----- mat/domace_naloge/26/dokument.pdf | Bin 57785 -> 64025 bytes mat/domace_naloge/26/dokument.synctex.gz | Bin 18248 -> 26595 bytes mat/domace_naloge/26/dokument.tex | 14 ++ mat/domace_naloge/26/stderr.log | 2 +- mat/domace_naloge/26/stdout.log | 182 ++++++++++++++------------ "mat/domace_naloge/26/\305\276" | 211 +++++++++++++++++++++++++++++++ 8 files changed, 369 insertions(+), 113 deletions(-) create mode 100644 "mat/domace_naloge/26/\305\276" diff --git a/mat/domace_naloge/26/dokument.aux b/mat/domace_naloge/26/dokument.aux 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}{} \babel@aux{slovene}{} \@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 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex 2020.12.21) 21 FEB 2021 00:07 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex 2020.12.21) 21 FEB 2021 21:03 entering extended mode \write18 enabled. %&-line parsing enabled. @@ -1767,61 +1767,70 @@ LaTeX Font Info: Trying to load font information for U+msb on input line 134 (/usr/local/texlive/2020/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) -Overfull \hbox (6.69476pt too wide) in paragraph at lines 185--185 +Overfull \hbox (6.69476pt too wide) in paragraph at lines 191--191 []|\OT1/cmr/m/n/10 v ena-ko-strani^^Tcnem tri-ko-tniku s stra-nico, dolgo [][], [] -Overfull \hbox (6.69476pt too wide) in paragraph at lines 185--185 +Overfull \hbox (6.69476pt too wide) in paragraph at lines 191--191 |\OT1/cmr/m/n/10 v ena-ko-strani^^Tcnem tri-ko-tniku s stra-nico, dolgo [][], [] -Overfull \hbox (1.88957pt too wide) in paragraph at lines 185--185 +Overfull \hbox (1.88957pt too wide) in paragraph at lines 191--191 |\OT1/cmr/m/n/10 v pra-vo-ko-tniku s stra-ni-cama, dol-gima [][] in [][], [] -Package hyperref Warning: Composite letter `\textasciicaron+c' -(hyperref) not defined in PD1 encoding, -(hyperref) removing `\textasciicaron' on input line 191. +Overfull \hbox (6.63931pt too wide) detected at line 191 +[] \OMS/cmsy/m/n/10 ^^A [] \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 j[]j ^^A j[]j ^^A + [] [][]\OT1/cmr/m/n/10 11\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 926966 + [] [1 {/usr/local/texlive/2020/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] + +Package hyperref Warning: Composite letter `\textasciicaron+c' +(hyperref) not defined in PD1 encoding, +(hyperref) removing `\textasciicaron' on input line 205. + [2] (./dokument.aux) Package rerunfilecheck Info: File `dokument.out' has not changed. (rerunfilecheck) Checksum: 8100D3BBD9090570F4741E21DDC77BBB;44. ) Here is how much of TeX's memory you used: - 44276 strings out of 479382 - 1042757 string characters out of 5869354 - 1560916 words of memory out of 5000000 - 60412 multiletter control sequences out of 15000+600000 + 44278 strings out of 479382 + 1042774 string characters out of 5869354 + 1561039 words of memory out of 5000000 + 60414 multiletter control sequences out of 15000+600000 417199 words of font info for 80 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 - 94i,15n,118p,1061b,1266s stack positions out of 5000i,500n,10000p,200000b,80000s - - -Output written on dokument.pdf (2 pages, 173797 bytes). + 94i,16n,118p,1061b,1266s stack positions out of 5000i,500n,10000p,200000b,80000s +{/usr/local/texlive/2020/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc +} +< +/usr/local/texlive/2020/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx9.pfb> +Output written on dokument.pdf (2 pages, 186927 bytes). PDF statistics: - 137 PDF objects out of 1000 (max. 8388607) - 100 compressed objects within 1 object stream + 147 PDF objects out of 1000 (max. 8388607) + 107 compressed objects within 2 object streams 17 named destinations out of 1000 (max. 500000) 117 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/mat/domace_naloge/26/dokument.pdf b/mat/domace_naloge/26/dokument.pdf index 36f2f01..e422053 100644 Binary files a/mat/domace_naloge/26/dokument.pdf and b/mat/domace_naloge/26/dokument.pdf differ diff --git a/mat/domace_naloge/26/dokument.synctex.gz b/mat/domace_naloge/26/dokument.synctex.gz index 3c0a2d7..29d69dc 100644 Binary files a/mat/domace_naloge/26/dokument.synctex.gz and b/mat/domace_naloge/26/dokument.synctex.gz differ 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 diff --git a/mat/domace_naloge/26/stderr.log b/mat/domace_naloge/26/stderr.log index a569f42..393e7ee 100644 --- a/mat/domace_naloge/26/stderr.log +++ b/mat/domace_naloge/26/stderr.log @@ -1 +1 @@ -<]/Index[ 0 138]/Info 136 0 R/Length 356/Root 135 0 R/Size 138/W[ 1 3 1]>> +<]/Index[ 0 148]/Info 146 0 R/Length 378/Root 145 0 R/Size 148/W[ 1 3 1]>> diff --git a/mat/domace_naloge/26/stdout.log b/mat/domace_naloge/26/stdout.log index a422ed7..a50f3bc 100644 --- a/mat/domace_naloge/26/stdout.log +++ b/mat/domace_naloge/26/stdout.log @@ -526,40 +526,47 @@ onary-English.dict) (/usr/local/texlive/2020/texmf-dist/tex/latex/exsheets/exsheets_configurations. cfg) (/usr/local/texlive/2020/texmf-dist/tex/latex/amsfonts/umsa.fd) (/usr/local/texlive/2020/texmf-dist/tex/latex/amsfonts/umsb.fd) -Overfull \hbox (6.69476pt too wide) in paragraph at lines 185--185 +Overfull \hbox (6.69476pt too wide) in paragraph at lines 191--191 []|\OT1/cmr/m/n/10 v ena-ko-strani^^Tcnem tri-ko-tniku s stra-nico, dolgo [][], -Overfull \hbox (6.69476pt too wide) in paragraph at lines 185--185 +Overfull \hbox (6.69476pt too wide) in paragraph at lines 191--191 |\OT1/cmr/m/n/10 v ena-ko-strani^^Tcnem tri-ko-tniku s stra-nico, dolgo [][], -Overfull \hbox (1.88957pt too wide) in paragraph at lines 185--185 +Overfull \hbox (1.88957pt too wide) in paragraph at lines 191--191 |\OT1/cmr/m/n/10 v pra-vo-ko-tniku s stra-ni-cama, dol-gima [][] in [][], +Overfull \hbox (6.63931pt too wide) detected at line 191 +[] \OMS/cmsy/m/n/10 ^^A [] \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 j[]j ^^A j[]j ^^A + [] [][]\OT1/cmr/m/n/10 11\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 926966 +[1{/usr/local/texlive/2020/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] + Package hyperref Warning: Composite letter `\textasciicaron+c' (hyperref) not defined in PD1 encoding, -(hyperref) removing `\textasciicaron' on input line 191. +(hyperref) removing `\textasciicaron' on input line 205. -[1{/usr/local/texlive/2020/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2] (./dokument.aux) ) -(see the transcript file for additional information) -Output written on dokument.pdf (2 pages, 173797 bytes). +(see the transcript file for additional information){/usr/local/texlive/2020/te +xmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc} +Output written on dokument.pdf (2 pages, 186927 bytes). 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/home/a/Documents/sola-gimb-2/mat/domace_naloge/26/dokument-uncompressed.pdf **** 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/\305\276" "b/mat/domace_naloge/26/\305\276" new file mode 100644 index 0000000..04b062a --- /dev/null +++ "b/mat/domace_naloge/26/\305\276" @@ -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} -- cgit v1.2.3