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      <text>9.5.4.3 Plane equation, example</text>
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      <text><![CDATA[<h4 class="HELM_example">Example</h4>
<ol class="HELM_parts_inline">
<li>Find the vector equation of the plane which passes through the point with position vector \(3\underline{ i}+2\underline{ j}+5\underline{ k}\) and which is perpendicular to \(\underline{i}+\underline{k}.\)</li><p></p>
<p>
</p><li>Find the Cartesian equation of this plane.</li>
</ol>
<p></p>
<h4 class="HELM_solution">Solution</h4>
<ol class="HELM_parts">
  <li>Using the previous results we can write down the equation <span class="math inline">\(\qquad 
\underline{ r}\cdot(\underline{i}+\underline{k})=
(3\underline{ i}+2\underline{ j}+5\underline{ k})\cdot(\underline{i}+\underline{k})=3+5=8.\)</span> </li>
  <li> Writing <span class="math inline">\(\underline{ r}\)</span> as <span class="math inline">\(x\underline{ i}+y\underline{ j}+z\underline{ k}\)</span> we have the Cartesian form: <span class="math inline">\(\qquad
(x\underline{ i}+y\underline{ j}+z\underline{ k})\cdot
(\underline{i}+\underline{k})=8\)</span> so that <span class="math inline">\(\qquad 
x+z=8\)</span>.</li>
</ol>]]></text>
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