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    <name>
      <text>9.5.3.6 Cartesian form, Example</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<h4 class="HELM_example">Example</h4>
<ol class="HELM_parts_inline">
<li>Write down the Cartesian form of the equation of the straight line which passes through the two points <span class="math inline">\((9,3,-2)\)</span> and <span class="math inline">\((4,5,-1)\)</span>.</li><p></p>
<li>State the equivalent vector equation.</li>
</ol>

<h4 class="HELM_solution">Solution</h4>
<ol class="HELM_parts">
  <li>The Cartesian equation of the line is \(\dfrac{x-9}{4-9}=\dfrac{y-3}{5-3}= \dfrac{z-(-2)}{-1-(-2)},\) that is \(\dfrac{x-9}{-5}= \dfrac{y-3}{2} = \dfrac{z+2}{1}.\) </li>
  <li>The vector equation of the line is \[
\underline{ r}=\underline{ a} +t(\underline{ b}-\underline{ a})\]
\[=
\begin{bmatrix}
9 \\  3 \\  -2 
\end{bmatrix} + t\left(
\begin{bmatrix}
4 \\  5 \\  -1
\end{bmatrix}-
\begin{bmatrix}
9 \\  3 \\  -2 
\end{bmatrix}\right)\]\[=\begin{bmatrix}
9 \\  3 \\  -2 
\end{bmatrix} + t
\begin{bmatrix}
-5 \\ 2 \\1
\end{bmatrix}.\]</li>
</ol>]]></text>
    </questiontext>
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