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<body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Normalkomponente rootpage-Normalkomponente skin-vector-2022 action-view">
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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Normalkomponente</span></h1>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>Einen <a href="Vektor" title="Vektor">Vektor</a> im dreidimensionalen Raum <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{3}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
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<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">R</mi>
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<mn>3</mn>
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<annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{3}}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f936ddf584f8f3dd2a0ed08917001b7a404c10b5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.732ex; height:2.676ex;" alt="{\displaystyle \mathbb {R} ^{3}}" loading="lazy"></span> kann man in Bezug auf eine Richtung oder eine Ebene eindeutig in eine Parallelkomponente und eine <b>Normalkomponente</b> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}_{\perp }}">
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<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>a</mi>
<mo stretchy="false">→<!-- → --></mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>⊥<!-- ⊥ --></mo>
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<annotation encoding="application/x-tex">{\displaystyle {\vec {a}}_{\perp }}</annotation>
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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8ae375792d559240167074b0493a7f6ec8b889ba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.741ex; height:2.676ex;" alt="{\displaystyle {\vec {a}}_{\perp }}" loading="lazy"></span> zerlegen:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}={\vec {a}}_{\parallel }+{\vec {a}}_{\perp }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
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<mover>
<mi>a</mi>
<mo stretchy="false">→<!-- → --></mo>
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<mo>=</mo>
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<mover>
<mi>a</mi>
<mo stretchy="false">→<!-- → --></mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>∥<!-- ∥ --></mo>
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<mo>+</mo>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>a</mi>
<mo stretchy="false">→<!-- → --></mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>⊥<!-- ⊥ --></mo>
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<annotation encoding="application/x-tex">{\displaystyle {\vec {a}}={\vec {a}}_{\parallel }+{\vec {a}}_{\perp }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bedce53fa7a7469feacf14b103bec2f7b5db8fb0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:12.193ex; height:3.176ex;" alt="{\displaystyle {\vec {a}}={\vec {a}}_{\parallel }+{\vec {a}}_{\perp }}" loading="lazy"></span></dd></dl>
<p>Darin ist
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>a</mi>
<mo stretchy="false">→<!-- → --></mo>
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</mrow>
</mrow>
</mstyle>
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<annotation encoding="application/x-tex">{\displaystyle {\vec {a}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/546e6615827e17295718741fd0b86f639a947f16.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:2.343ex;" alt="{\displaystyle {\vec {a}}}" loading="lazy"></span>: ein beliebiger Vektor im <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{3}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">R</mi>
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<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
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</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{3}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f936ddf584f8f3dd2a0ed08917001b7a404c10b5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.732ex; height:2.676ex;" alt="{\displaystyle \mathbb {R} ^{3}}" loading="lazy"></span></dd>
<dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}_{\parallel }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>a</mi>
<mo stretchy="false">→<!-- → --></mo>
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</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>∥<!-- ∥ --></mo>
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</mstyle>
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<annotation encoding="application/x-tex">{\displaystyle {\vec {a}}_{\parallel }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e8789b8c69f6977c3faee7ea0838cfd1063ca2a4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.284ex; height:3.176ex;" alt="{\displaystyle {\vec {a}}_{\parallel }}" loading="lazy"></span>: ein Vektor parallel zur gewählten Richtung bzw. <a href="Tangentialebene" title="Tangentialebene">Ebene</a></dd>
<dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {a}}_{\perp }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>a</mi>
<mo stretchy="false">→<!-- → --></mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>⊥<!-- ⊥ --></mo>
</mrow>
</msub>
</mstyle>
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<annotation encoding="application/x-tex">{\displaystyle {\vec {a}}_{\perp }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8ae375792d559240167074b0493a7f6ec8b889ba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.741ex; height:2.676ex;" alt="{\displaystyle {\vec {a}}_{\perp }}" loading="lazy"></span>: ein Vektor senkrecht zur gewählten Richtung bzw. Ebene.</dd></dl>
<p>Die Zerlegung setzt <i>nicht</i> voraus, dass ein bestimmtes <a href="Koordinatensystem" title="Koordinatensystem">Koordinatensystem</a> definiert ist.
</p>
<div class="mw-heading mw-heading2"><h2 id="Siehe_auch">Siehe auch</h2></div>
<ul><li><a href="Normalenvektor" title="Normalenvektor">Normalenvektor</a></li>
<li><a href="Richtungsvektor" class="mw-redirect" title="Richtungsvektor">Richtungsvektor</a></li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
Dieser Artikel wurde von <a class="external text" title="Zuletzt bearbeitet am 2020-02-15" href="https://de.wikipedia.org/wiki/?title=Normalkomponente&oldid=196832922">Wikipedia</a> herausgegeben. Der Text ist unter <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.de">Creative Commons Attribution-Share Alike 4.0</a> verfügbar, sofern nicht anders angegeben. Für die Mediendateien können zusätzliche Bedingungen gelten.
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