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+%-----------------------------------------------------------------------------
+% Copyright (C) 2004-2019 Andrew Mathas, University of Sydney
+%
+% Distributed under the terms of the GNU General Public License (GPL)
+% http://www.gnu.org/licenses/
+%
+% This file is part of the WebQuiz system.
+%
+% <Andrew.Mathas@sydney.edu.au>
+%-----------------------------------------------------------------------------
+
+%% This file is part of the WebQuiz class distribution
+\PassOptionsToClass{svgnames}{xcolor}
+\documentclass[svgnames]{webquiz}
+
+% load webquiz-doc code -- the class file loads webquiz-ini.code.tex is first
+\input{webquiz-doc.code}
+
+% using \textcolor or \color in \WebQuiz conflicts with the code to make
+% listings respect color in webquiz.cfg
+\newcommand\WebQuiz{WebQuiz\xspace}
+
+\usepackage{pst-plot}
+\usepackage{hyperref}
+
+\usepackage{ifpdf}
+\ifpdf
+ \PackageError{WebQuiz}{This file must be compiled using latex not pdflatex}
+\fi
+\newcommand{\C}{\mathbb C}
+\newcommand*{\vect}[1]{\mathbf{#1}}
+
+\hypersetup{pdftitle={WebQuiz online manual}}
+
+\title{WebQuiz: Web Quizzes using LaTeX}
+\begin{document}
+
+\begin{discussion}[Introduction]
+ \WebQuiz is a \LaTeX{} package for creating \textit{interactive}
+ web quizzes. The idea is that you write the quiz using \LaTeX{} and that
+ \WebQuiz creates the web page from this file. Anything that you can
+ write using \LaTeX{} will be converted to \HTML by \WebQuiz. This
+ includes, for example, mathematics and graphics written using
+ \ctan{pstricks}. \WebQuiz supports three different types of quiz
+ questions:
+
+ \begin{enumerate}
+ \item Multiple choice questions with a \emph{unique} correct answer.
+ (See \qref{question1})
+ \item Multiple choice questions with \emph{several} (or no)
+ correct answers.
+ (See \qref{question2})
+ \item Questions that require the student to enter an answer, which
+ can then be compared with the correct answer in several different
+ ways. (See \qref{question3})
+ \end{enumerate}
+The use of \WebQuiz is described in the next section. Later
+sections describe how each of the \WebQuiz environments are used.
+
+The \LatexCode|discussion| environment in \WebQuiz can also be used to
+write Web Pages like this one (The pages you are reading here were
+written using \WebQuiz.)
+\end{discussion}
+\begin{discussion}[Basic Usage]
+Once you have a \WebQuiz file, you can run it through \LaTeX, in
+the usual way, to produce a readable version of your quiz. When you
+are happy with the quiz, use \WebQuiz to create the HTML
+version. Note that the printable version of the quiz does \emph{not}
+look like the web page; rather, it contains all of the information in
+an easily readable layout.
+
+ If, for example, your quiz file is called \emph{quiz1.tex} then you
+ can use the following commands:
+\begin{latexcode}
+ > latex quiz1 % latex a quiz file
+ > pdflatex quiz1 % a PDF versio of the quiz
+ > xdvi quiz1 % view the quiz using xdvi
+ > dvips quiz1 % print the quiz
+ > webquiz quiz1 % converts the quiz to html
+\end{latexcode}
+ Converting the quiz to html can take quite a long time, particularly
+ if a large number of images need to be created.
+
+\end{discussion}
+\begin{discussion}[WebQuiz files]
+
+ The basic structure of a \WebQuiz file is as follows:
+\begin{latexcode}
+ \documentclass{webquiz}
+
+ \title{Quiz 1: Complex numbers}
+
+ \UnitCode{MATH1001}
+ \UnitName{Differential Calculus}
+ \UnitURL{/u/UG/JM/MATH1001/}
+ \QuizzesURL{/u/UG/JM/MATH1001/Quizzes/}
+
+ \begin{document}
+
+ \begin{discussion}[short heading][optional heading]
+ . . . % optional discussion
+ \end{discussion}
+
+ \begin{question} % question 1
+ . . .
+ \end{question}
+
+ \begin{question} % question 2
+ . . .
+ \end{question}
+ .
+ .
+ \end{document}
+\end{latexcode}
+ In the preamble of the \LaTeX{} file you can specify the unit code, the
+ name of the unit of study, the location of the homepage for the
+ unit and the index file for the quizzes for this unit; this is
+ done using the commands
+ \LatexCode|\UnitCode|,
+ \LatexCode|\UnitName|,
+ \LatexCode|\UnitURL| and
+ \LatexCode|\QuizzesURL| respectively. If the
+ command \LatexCode|\QuizzesURL| is omitted then the URL for the quiz
+ index file is set to \LatexCode|\UnitURL/|Quizzes.
+
+ The title of the quiz can be set in the preamble using the
+ \LatexCode|\title| command. Note that the \LatexCode|\title|
+ command \emph{must} appear before the \LatexCode|\begin{document}| command.
+ As in any \LaTeX{} document, the preamble can define macros and load
+ other \LaTeX{} packages the usual way .
+
+ By using the \LatexCode|discussion| environment you can summarise the
+ material for the students or add introductory material for the quiz.
+ For example, \LatexCode|discussion| environments can be used to recall
+ that main concepts being covered by the quiz or to give references to
+ the lecture notes for the unit. The syntax for the
+ \LatexCode|discussion| environment is as follows:
+\begin{latexcode}
+ \begin{discussion}[optional short heading][optional heading]
+ . . .
+ \end{discussion}
+\end{latexcode}
+ Anything you like (text, mathematics, \ldots) can go inside
+ discussion environments. The \emph{optional heading}, which defaults
+ to Discussion'', is used both as
+ the section heading on the web page and as the heading in the
+ side-menu on left hand side of the page. If a \textit{short heading}
+ is also given then it is used in the side-menu. The quiz can contain
+ zero or more discussion items ( and zero or more quiz questions).
+
+ Questions are set inside a \LatexCode|question| environment. The text is
+ followed by the answers.
+
+ \WebQuiz supports three types of questions:
+ \begin{itemize}
+ \item Multiple choice questions with \emph{precisely one} correct
+ answer;
+ \item Multiple choice questions with \emph{zero or more } correct
+ answers;
+ \item Questions that require the students to enter an answer. Five
+ difference comparison methods are available.
+ \end{itemize}
+ With each of these types of questions you can (and should) provide
+ feedback to the students depending on whether their answer is
+ correct or incorrect. Below we describe how to produce these
+ different types of questions.
+\end{discussion}
+\begin{discussion}[Question 1]
+ The syntax for a multiple choice question having \emph{precisely
+ one} correct answer is as follows:
+\begin{latexcode}
+ \begin{question}
+ . . .question text
+ \begin{choice}
+ \(in)correct . . . text for (in)correct option
+ \feedback . . . feedback on response
+
+ \(in)correct . . . text for (in)correct option
+ \feedback . . . feedback on response
+ .
+ .
+ .
+ \end{choice}
+ \end{question}
+\end{latexcode}
+ The different choices in a multiple choice question must be inside a
+ \LatexCode|choice| environment. This environment behaves like a
+ standard \LaTeX{} list environment except that instead of using
+ \LatexCode|\item| for list item you use:
+ \begin{itemize}
+ \item \LatexCode|\correct| for a correct choice
+ \item \LatexCode|\incorrect| for an incorrect choice
+ \item \LatexCode|\feedback| to give feedback to the student when
+ they select this choice
+ \end{itemize}
+ At most one \LatexCode|\feedback| response should be given for each
+ \LatexCode|\correct| and each \LatexCode|\incorrect| response.
+ The \LatexCode|\feedback| commands are optional; however, it is
+ recommended that you use them because targeted feedback to the
+ students based on their responses can be beneficial.
+ \par
+ For example, the code below, when run through \WebQuiz, produces \qref{question1}
+ in the online manual quiz.
+\begin{latexcode}
+ \begin{question}
+ The shaded region in the graph
+ \begin{center}
+ \begin{pspicture}(-3,-1.5)(3,4)
+ \pscircle[linewidth=1pt,linestyle=dashed,%
+ fillcolor=SkyBlue,fillstyle=solid](1,1){2}
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {->}(0,0)(-1.5,-1.5)(3.5,3.5)
+ \rput(3.75,0){$x$}
+ \rput(0,3.85){$iy$}
+ \rput(3,-0.4){3}
+ \rput(-0.4,3){3$i$}
+ \psdots(1,1)
+ \end{pspicture}
+ \end{center}
+ is equal to which of the following sets of complex numbers?
+ \begin{choice}
+ \incorrect $\{z \in \C : (z-1)^{2}+(z-(i+1))^{2}<2\}$
+ \feedback The equation of a circle in the complex plane with
+ centre $a+ib$ and radius $r$ is
+ \begin{displaymath}
+ \{z\in\C : |z-(a+ib)|<r \}.
+ \end{displaymath}
+
+ \incorrect $\{z \in \C : z+(i+1)<2\}$
+ \feedback You want the set of points whose \textit{distance}
+ from $1+i$ is less than $2$.
+
+ \correct $\{z \in \C : |z-(i+1)|<2\}$
+ \feedback The graph shows the set of complex numbers whose
+ distance from $1+i$ is less than $2$.
+
+ \incorrect $\{z \in \C : |z-2|<|i+1-2|\}$
+ \feedback As $|i+1-2|=\sqrt 2$, this is the set of complex
+ numbers whose distance from $2$ is less than
+ $\sqrt 2$.
+
+ \incorrect None of the above.
+ \feedback The graph shows the set of complex numbers whose
+ distance from the centre of the circle is less than $2$.
+ \end{choice}
+ \end{question}
+\end{latexcode}
+\end{discussion}
+\begin{discussion}[Question 2]
+ To allow multiple (or no) correct answer we add \LatexCode|multiple| as an
+ optional argument to the \LatexCode|choice| environment:
+\begin{latexcode}
+ \begin{question}
+ . . .question text. . .
+ \begin{choice}[multiple]
+ \(in)correct . . . text for (in)correct option
+ \feedback . . . feedback on response
+
+ \(in)correct . . . text for (in)correct option
+ \feedback . . . feedback on response
+ .
+ .
+ .
+ \end{choice}
+ \end{question}
+\end{latexcode}
+ The only difference to the previous case is that zero or more
+ \LatexCode|\correct| commands can appear.
+ \par
+ For example, \qref{question2} below was typed into \WebQuiz
+ using the following commands:
+\begin{latexcode}
+ \begin{question}
+ Which of the following numbers are prime?
+ \begin{choice}[multiple]
+ \incorrect 1
+ \feedback By definition, a prime is a number greater than 1
+ whose only factors are 1 and itself.
+
+ \correct 19
+ \feedback The only factors of 19 are 1 and itself.
+
+ \incorrect 6
+ \feedback 2 is a factor of 6
+
+ \correct 23
+ \feedback The only factors of 23 are 1 and itself.
+
+ \correct 191
+ \feedback The only factors of 191 are 1 and itself.
+ \end{choice}
+ \end{question}
+\end{latexcode}
+\end{discussion}
+\begin{discussion}[Question 3]
+
+ By default, the \LatexCode|choice| environments puts the multiple
+ choice options into one column format. Sometimes the options look
+ better when listed in two or more columns, however, this should be
+ used sparingly as multiple columns do not always display well if the
+ quiz is viewed on a mobile device. By using the \LatexCode|columns|
+ key word in a \LatexCode|choice| environment you can specify the
+ number of columns in the HTML version of the quiz.
+
+\begin{latexcode}
+ \begin{question}
+ . . .question text. . .
+ \begin{choice}[multiple, columns=n] . . . n columns
+ \(in)correct . . . text for (in)correct option
+ \feedback . . . feedback on response
+
+ \(in)correct . . . text for (in)correct option
+ \feedback . . . feedback on response
+ .
+ .
+ .
+ \end{choice}
+ \end{question}
+\end{latexcode}
+ If the optional argument \LatexCode|[multiple]| is not present, then the
+ question admits precisely one correct answer.
+ \par
+ For example, \qref{question3} below was typed into \WebQuiz
+ using the following commands:
+\begin{latexcode}
+ \begin{question}
+ What are suitable parametric equations for this plane curve?
+ \begin{center}
+ \psset{unit=.6cm}
+ \begin{pspicture}(-2.5,-0.5)(5,5.5)
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {->}(0,0)(-2.5,-1.5)(5,5)
+ \psellipse[linecolor=SkyBlue,linewidth=2pt](1,2)(3,2)
+ \end{pspicture}
+ \end{center}
+
+ \begin{choice}[columns=1]
+ \incorrect $x=2\cos t + 1$, $y=3\sin t + 2$
+ \feedback This is an ellipse with centre $(1,2)$ and with axes of
+ length $4$ in the $x$-direction and $6$ in the $y$-direction.
+ \begin{center}
+ \psset{unit=.6cm}
+ \begin{pspicture}(-2.5,-0.5)(5,5.5)
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {->}(0,0)(-2.5,-1.5)(5,5)
+ \parametricplot[linecolor=SkyBlue,linewidth=2pt]{0}{360}%
+ {t cos 2 mul 1 add t sin 3 mul 2 add}
+ \end{pspicture}
+ \end{center}
+
+ \correct $x=3\cos t + 1$, $y=2\sin t + 2$
+ \feedback The curve is an ellipse centre (1,2) with axes length 6
+ in the $x$ direction and 4 in the $y$ direction.
+
+ \incorrect $x=3\cos t - 1$, $y=2\sin t - 2$
+ \feedback This is an ellipse with centre $(-1,-2)$ and with axes
+ of length $6$ in the $x$-direction and $4$ in the $y$-direction.
+ \begin{center}
+ \psset{unit=.6cm}
+ \begin{pspicture}(-5,-4)(1,2)
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {<-}(0,0)(-4.5,-5.5)(1,2)
+ \parametricplot[linecolor=SkyBlue,linewidth=2pt]{0}{360}%
+ {t cos 3 mul 1 sub t sin 2 mul 2 sub}
+ \end{pspicture}
+ \end{center}
+
+ \incorrect $x=2\cos t - 1$, $y=3\sin t - 2$
+ \feedback This is an ellipse with centre $(-1,-2)$ and with axes
+ of length $4$ in the $x$-direction and $6$ in the $y$-direction.
+ \begin{center}
+ \psset{unit=.6cm}
+ \begin{pspicture}(-4,-5)(1,2)
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {<-}(0,0)(-4.5,-5.5)(1,2)
+ \parametricplot[linecolor=SkyBlue,linewidth=2pt]{0}{360}%
+ { t cos 2 mul 1 sub t sin 3 mul 2 sub}
+ \end{pspicture}
+ \end{center}
+ \end{choice}
+ \end{question}
+\end{latexcode}
+\end{discussion}
+\begin{discussion}[Question 4]
+ The final type of question that \WebQuiz supports is a question that
+ requires an answer, which can be a number or a string. The answer is
+ typeset using the \LatexCode|\answer| macro. The \LatexCode|\answer|
+ macro takes two arguments: an optional comparison method, which
+ defaults to \LatexCode|string|, and the correct answer for the
+ question:
+ \begin{latexcode}
+ \answer[comparison method]{correct answer}
+ \end{latexcode}
+ Feedback for correct and incorrect answers is given
+ using the macros \LatexCode|\whenRight| and \LatexCode|\whenWrong|,
+ respectively. The structure of questions with \LatexCode|\answer|'s is as follows:
+ \begin{latexcode}
+ \begin{question}
+ . . .question text. . .
+ \answer[*][complex|integer|lowercase|number|string]{actual answer}
+ \whenRight . . . feedback when right (optional)
+ \whenWrong . . . feedback when wrong (optional)
+ \end{question}
+ \end{latexcode}
+ See the \WebQuiz manual for details of the different
+ comparison types. For example, \qref{question4} below was typed into
+ \WebQuiz using the following commands:
+\begin{latexcode}
+ \begin{question}
+ If the vectors $\vect{a}$ (of magnitude 8 units) and $\vect{b}$
+ (of magnitude 3 units) are perpendicular, what is the value
+ of
+ \begin{displaymath}
+ |\vect{a} -2\vect{b}|~?
+ \end{displaymath}
+ (Hint: Draw a diagram!)
+
+ \answer[number]{10}
+ \whenRight The vectors $\vect{a}$, \(-2\vect{b}\), and
+ $\vect{a} - 2\vect{b}$ form the sides of a right-angled
+ triangle, with sides of length $8$ and $6$ and
+ hypotenuse of length $|\vect{a} -2\vect{b}|$. Therefore
+ by Pythagoras' Theorem,
+ \(|\vect{a} -2\vect{b}|=\sqrt{8^2+6^2}=10\).
+
+ \whenWrong Draw a diagram and then use Pythagoras' theorem.
+ \end{question}
+\end{latexcode}
+\end{discussion}
+\begin{discussion}[Index Files]
+ \WebQuiz also provides a mechanism for creating a web page
+ containing an index of all quizzes for a given Unit of Study.
+ This is done with a \WebQuiz file that contains a \LatexCode|quizindex|
+ environment. The syntax for this environment is as follows:
+\begin{latexcode}
+ \begin{quizindex}
+ \quiz[url1]{title for quiz 1}
+ \quiz[url2]{title for quiz 2}
+ . . .
+ \end{quizindex}
+\end{latexcode}
+If no \textit{URL} is given as an optional argument to
+\LatexCode|\quiz| then
+ \WebQuiz sets the url(s) to \BashCode|quiz1.html|, \BashCode|quiz2.html|
+ and so on.
+\end{discussion}
+
+\begin{discussion}[Credits]
+ \WebQuiz was written and developed in the
+ \href{http://www.maths.usyd.edu.au/}{School of Mathematics and
+ Statistics} at the \href{http://www.usyd.edu.au/}{University of
+ Sydney}. The system is built on \LaTeX{} with the conversion from
+ \LaTeX{} to HTML using Eitan Gurari's
+ \href{http://www.cis.ohio-state.edu/~gurari/TeX4ht/mn.html}{TeX4ht},
+ and Michal Hoftich's
+ \href{https://github.com/michal-h21/make4ht}{make4ht}.
+
+ To write quizzes using \WebQuiz it is only necessary to know
+ \LaTeX, however, the \WebQuiz system has three components:
+ \begin{itemize}
+ \item A \LaTeX{} document class file, \LatexCode{webquiz.cls}, and
+ a \TeXfht configuration file, \LatexCode{webquitexz.cfg}, that enable the
+ quiz files to be processed by \LaTeX{} and \TeXfht, respectively.
+ \item A python program, \BashCode{webquiz}, that translates the \XML
+ file that is produced by \TeXfht into \HTML.
+ \item Some \Javascript and \CSS that controls the quiz web page.
+ \end{itemize}
+
+ The \LaTeX{} component of \WebQuiz was written by Andrew Mathas and
+ the python, \CSS and \Javascript code was written by Andrew Mathas (and
+ Don Taylor), based on an initial prototype of Don Taylor's from 2001.
+ Since 2004 the program has been maintained and developed by Andrew
+ Mathas. Although the program has changed substantially since 2004,
+ Don's idea of using \TeXfht, and some of his code, is still in use.
+
+ Thanks are due to Bob Howlett for general help with CSS and, for
+ Version~5, to Michal Hoftich for technical advice.
+\end{discussion}
+
+\begin{question}
+ \label{question1}
+ The shaded region in the graph
+ \begin{center}
+ \begin{pspicture}(-3,-1.5)(3,4)
+ \pscircle[linewidth=1pt,linestyle=dashed,fillcolor=SkyBlue,fillstyle=solid](1,1){2}
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {->}(0,0)(-1.5,-1.5)(3.5,3.5)
+ \rput(3.75,0){$x$}
+ \rput(0,3.85){$iy$}
+ \rput(3,-0.4){3}
+ \rput(-0.4,3){3$i$}
+ \psdots(1,1)
+ \end{pspicture}
+ \end{center}
+ is equal to which of the following sets of complex numbers?
+ \begin{choice}
+ \incorrect $\{z \in \C : (z-1)^{2}+(z-(i+1))^{2}<2\}$
+ \feedback The equation of a circle in the complex plane with
+ centre $a+ib$ and radius $r$ is
+ \begin{displaymath}
+ \{z\in\C : |z-(a+ib)|<r \}.
+ \end{displaymath}
+
+ \incorrect $\{z \in \C : z+(i+1)<2\}$
+ \feedback You want the set of points whose \textit{distance}
+ from $1+i$ is less than $2$.
+
+ \correct $\{z \in \C : |z-(i+1)|<2\}$
+ \feedback The graph shows the set of complex numbers whose
+ distance from $1+i$ is less than $2$.
+
+ \incorrect $\{z \in \C : |z-2|<|i+1-2|\}$
+ \feedback As $|i+1-2|=\sqrt 2$, this is the set of complex
+ numbers whose distance from $2$ is less than
+ $\sqrt 2$.
+
+ \incorrect None of the above.
+ \feedback The graph shows the set of complex numbers whose
+ distance from the centre of the circle is less than $2$.
+ \end{choice}
+\end{question}
+
+\begin{question}
+ \label{question2}
+ Which of the following numbers are prime?
+ \begin{choice}[multiple]
+ \incorrect 1
+ \feedback By definition, a prime is a number greater than 1
+ whose only factors are 1 and itself.
+
+ \correct 19
+ \feedback The only factors of 19 are 1 and itself.
+
+ \incorrect 6
+ \feedback 2 is a factor of 6
+
+ \correct 23
+ \feedback The only factors of 23 are 1 and itself.
+
+ \correct 191
+ \feedback The only factors of 191 are 1 and itself.
+ \end{choice}
+\end{question}
+
+\begin{question}
+ \label{question3}
+ What are suitable parametric equations for this plane curve?
+ \begin{center}
+ \psset{unit=.6cm}
+ \begin{pspicture}(-2.5,-0.5)(5,5.5)
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {->}(0,0)(-2.5,-1.5)(5,5)
+ \psellipse[linecolor=SkyBlue,linewidth=2pt](1,2)(3,2)
+ \end{pspicture}
+ \end{center}
+
+ \begin{choice}[columns=1]
+ \incorrect $x=2\cos t + 1$, $y=3\sin t + 2$
+ \feedback This is an ellipse with centre $(1,2)$ and with axes of
+ length $4$ in the $x$-direction and $6$ in the $y$-direction.
+ \begin{center}
+ \psset{unit=.6cm}
+ \begin{pspicture}(-2.5,-0.5)(5,5.5)
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {->}(0,0)(-2.5,-1.5)(5,5)
+ \parametricplot[linecolor=SkyBlue,linewidth=2pt]{0}{360}%
+ {t cos 2 mul 1 add t sin 3 mul 2 add}
+ \end{pspicture}
+ \end{center}
+
+ \correct $x=3\cos t + 1$, $y=2\sin t + 2$
+ \feedback The curve is an ellipse centre (1,2) with axes length 6
+ in the $x$ direction and 4 in the $y$ direction.
+
+ \incorrect $x=3\cos t - 1$, $y=2\sin t - 2$
+ \feedback This is an ellipse with centre $(-1,-2)$ and with axes
+ of length $6$ in the $x$-direction and $4$ in the $y$-direction.
+ \begin{center}
+ \psset{unit=.6cm}
+ \begin{pspicture}(-5,-4)(1,2)
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {<-}(0,0)(-4.5,-5.5)(1,2)
+ \parametricplot[linecolor=SkyBlue,linewidth=2pt]{0}{360}%
+ {t cos 3 mul 1 sub t sin 2 mul 2 sub}
+ \end{pspicture}
+ \end{center}
+
+ \incorrect $x=2\cos t - 1$, $y=3\sin t - 2$
+ \feedback This is an ellipse with centre $(-1,-2)$ and with axes
+ of length $4$ in the $x$-direction and $6$ in the $y$-direction.
+ \begin{center}
+ \psset{unit=.6cm}
+ \begin{pspicture}(-4,-5)(1,2)
+ \psaxes[linecolor=red,linewidth=1pt,labels=none]%
+ {<-}(0,0)(-4.5,-5.5)(1,2)
+ \parametricplot[linecolor=SkyBlue,linewidth=2pt]{0}{360}%
+ { t cos 2 mul 1 sub t sin 3 mul 2 sub}
+ \end{pspicture}
+ \end{center}
+ \end{choice}
+\end{question}
+
+\begin{question}
+ \label{question4}
+ If the vectors $\vect{a}$ (of magnitude 8 units) and $\vect{b}$
+ (of magnitude 3 units) are perpendicular, what is the value
+ of
+ \(|\vect{a} -2\vect{b}|\)~?
+ (Hint: Draw a diagram!)
+
+ \answer[number]{10} units
+ \whenRight The vectors $\vect{a}$, \(-2\vect{b}\), and
+ $\vect{a} - 2\vect{b}$ form the sides of a right-angled
+ triangle, with sides of length $8$ and $6$ and
+ hypotenuse of length $|\vect{a} -2\vect{b}|$. Therefore
+ by Pythagoras' Theorem,
+ \(|\vect{a} -2\vect{b}|=\sqrt{8^2+6^2}=10\).
+
+ \whenWrong Draw a diagram and then use Pythagoras' theorem.
+\end{question}
+\end{document}
+\endinput
+
+%% End of file `webquiz-manual.tex'.