<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>9.5.4.7 Perpendicular distance between plane and origin</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>What is the perpendicular distance from the origin to of the plane given by \(\underline{r}\cdot{@a1@}={@c1@}\)?</p>

<p>[[input:ans1]] [[validation:ans1]]</p>
[[feedback:prt1]]]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>By dividing through by \(\lvert\underline{n}\rvert = {@maga1@}\), we can express the equation of the plane as \({@stackvector(r)@}\cdot \underline{\hat{n}} =c\) where \(\underline{\hat{n}}\) is a unit vector parallel to \(\underline{n}\) and \(c\) is a constant.</p>
<p>Here \(\underline{\hat{n}} = \displaystyle{\frac{1}{{@maga1@}}{@a1@}}\) and \(c=\displaystyle{\frac{{@c1@}}{{@maga1@}}}\).</p>
<p>The distance between the plane and the origin is thus given by \(\displaystyle{{@h1@}}\).</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020120600</text>
    </stackversion>
    <questionvariables>
      <text><![CDATA[stackvectortex(ex):= block(sconcat("{ \\underline{", tex1(first(args(ex))), "}}"));
ordergreat(i,j,k);
a1: matrix([7],[7],[5]) - rand(matrix([3],[4],[2]));
maga1: sqrt(dotproduct(a1,a1));
c1: 7-rand(5);
h1: c1/maga1;]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>The distance from the plane to the origin is given by {@h1@};</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>h1</tans>
      <boxsize>10</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>h1</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>1578399687</deployedseed>
    <deployedseed>707307225</deployedseed>
    <deployedseed>2064314929</deployedseed>
    <deployedseed>661465317</deployedseed>
    <deployedseed>1128504441</deployedseed>
    <deployedseed>2049153565</deployedseed>
    <deployedseed>339768357</deployedseed>
    <deployedseed>854742259</deployedseed>
    <deployedseed>434622819</deployedseed>
    <deployedseed>1001742774</deployedseed>
    <deployedseed>907463674</deployedseed>
    <deployedseed>1607721965</deployedseed>
    <deployedseed>915053910</deployedseed>
    <deployedseed>1132488088</deployedseed>
    <deployedseed>1177899607</deployedseed>
    <deployedseed>992291957</deployedseed>
    <deployedseed>76477694</deployedseed>
    <deployedseed>1961864795</deployedseed>
    <deployedseed>522586823</deployedseed>
    <deployedseed>1840609713</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>h1</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>0</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty/>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
