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<title>A.II.4.33</title>
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<b>Feladat: 4.33.</b><br /> <a name="a_ii_linalg_061121_ha_02" /><a href="bib_box.php?mode=sne-s-j-&amp;citation_num=" target="bib_box" onclick="mutat('bib_box.php?mode=sne-s-j-&amp;citation_num='); return false;"></a><b>a)</b> Adjunk meg az <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:munder><m:mrow><m:mi>u</m:mi></m:mrow>

<m:mo stretchy="true">&OverBar;</m:mo></m:munder>

<m:mo stretchy="false">(</m:mo><m:mn>1</m:mn><m:mo>;</m:mo><m:mn>1</m:mn><m:mo>;</m:mo><m:mn>2</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math>,

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:munder><m:mrow><m:mi>v</m:mi></m:mrow>

<m:mo stretchy="true">&OverBar;</m:mo></m:munder>

<m:mo stretchy="false">(</m:mo><m:mn>2</m:mn><m:mo>;</m:mo><m:mn>3</m:mn><m:mo>;</m:mo><m:mo>-</m:mo><m:mn>1</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math> vektorokra merőleges vektort!

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<b>b)</b> Adjuk meg az összes ilyen vektort!
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<a name="_solution_a_ii_linalg_061121_ha_02" /><b>Megoldás: 4.33</b><br />
<b>a)</b> <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:munder><m:mrow><m:mi>w</m:mi></m:mrow>

<m:mo stretchy="true">&OverBar;</m:mo></m:munder>

<m:mo stretchy="false">(</m:mo><m:mn>7</m:mn><m:mo>;</m:mo><m:mo>-</m:mo><m:mn>5</m:mn><m:mo>;</m:mo><m:mo>-</m:mo><m:mn>1</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math>. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>b)</b>

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi mathvariant="italic">&lambda;</m:mi><m:mo>&middot;</m:mo>

<m:munder><m:mrow><m:mi>w</m:mi></m:mrow>

<m:mo stretchy="true">&OverBar;</m:mo></m:munder>

</m:mrow></m:math>, ahol <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi mathvariant="italic">&lambda;</m:mi></m:mrow></m:math> tetszőleges valós

szám.
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