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<quiz>
  <question type="stack">
    <name>
      <text>9.2.2.2 modulus of vectors (cartesian 3D)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise<br></p>
<p>Find the modulus of each of the following vectors (writing your answer in the form of a surd, i.e. \(\sqrt{x}\)):</p>
<ol class="HELM_parts">
<li><p> \(\underline{r} = {@a_vec@}, \quad |\underline{r}| = \)  [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p></li>
<li><p>\(\underline{s} = {@b_vec@}, \quad |\underline{s}| = \)  [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</p></li>
<li><p> \(\underline{t} = {@coefc1@}\underline{i} + {@coefc2@}\underline{j} - {@coefc3@}\underline{k}, \quad |\underline{t}| = \)  [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</p></li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Considering the general case in part (c), for the vector, \(\underline{t} = {@coefc1@}\underline{i} + {@coefc2@}\underline{j} - {@coefc3@}\underline{k}\) we calculate the modulus by applying Pythagoras' theorem: \(|\underline{t}| = \sqrt{{@coefc1@}^2 + {@coefc2@}^2 + (-{@coefc3@})^2}\).</p>
<p>By applying this we get:</p>
<p>For \(\underline{r} = {@a_vec@}, \quad |\underline{r}| = {@ta1@} .\)</p>
<p>For \(\underline{s} = -{@b_vec@}, \quad |\underline{s}| = {@ta2@}.\)</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2021072200</text>
    </stackversion>
    <questionvariables>
      <text><![CDATA[stack_reset_vars(true);
stackvectortex(ex):= block(sconcat("{\\underline{", tex1(first(args(ex))), "}}"));
ordergreat(i,j,k);
ijk_vec: matrix([i],[j],[k]);

a_2_sign:2*rand(2)-1;
b_2_sign:2*rand(2)-1;
a_3_sign:2*rand(2)-1;
b_3_sign:2*rand(2)-1;

sel: [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20];
picks:rand_selection(sel,6);
coefa1:picks[1];
coefa2:picks[2]*a_2_sign;
coefa3:picks[3]*a_3_sign;
a_mat:matrix([coefa1],[coefa2],[coefa3])
a_vec: texboldatoms(dotproduct(ijk_vec,a_mat));

coefb1:picks[4];
coefb2:picks[5]*b_2_sign;
coefb3:picks[6]*b_3_sign;
b_mat:matrix([coefb1],[coefb2],[coefb3])
b_vec: texboldatoms(dotproduct(ijk_vec,b_mat));

coefc1: a;
coefc2: b;
coefc3: c;

ta1:sqrt(coefa1^2+coefa2^2+coefa3^2);
ta2:sqrt(coefb1^2+coefb2^2+coefb3^2);
ta3:sqrt(coefc1^2+coefc2^2+coefc3^2);]]></text>
    </questionvariables>
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      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[\mathbf{r} = {@a_vec@}, \quad |\mathbf{r}| = {@ta1@} \]
\[\mathbf{s} = {@b_vec@}, \quad |\mathbf{s}| = {@ta2@}\]
\[\mathbf{t} = {@coefc1@}\mathbf{i} + {@coefc2@}\mathbf{j} - {@coefc3@}\mathbf{k}, \quad |\mathbf{t}| = {@ta3@}\]</text>
    </questionnote>
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      <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>none</multiplicationsign>
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    <complexno>i</complexno>
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        <text>neg_wrong:sqrt(coefa1^2 + (a_2_sign*(coefa2^2))+(a_3_sign*(coefa3^2)));</text>
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          <text><![CDATA[<p>When we calculate the modulus of the vector we take \(\sqrt{({@coefa1@})^2 + ({@coefa2@})^2 + ({@coefa3@})^2}\).<br></p>]]></text>
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          <text><![CDATA[<p>When we calculate the modulus of the vector we take \(\sqrt{({@coefb1@})^2 + ({@coefb2@})^2 + {@coefb3@}^2}\).<br></p>]]></text>
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          <text>When we calculate the modulus of the vector we take \(\sqrt{{@coefc1@}^2 + {@coefc2@}^2 + (-{@coefc3@})^2}\).</text>
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