<?xml version="1.0"?> <feed xmlns="http://www.w3.org/2005/Atom" xml:lang="ro"> <id>https://ro.wikibooks.org/w/index.php?action=history&amp;feed=atom&amp;title=Calcul_vectorial</id> <title>Calcul vectorial - Revizia istoricului</title> <link rel="self" type="application/atom+xml" href="https://ro.wikibooks.org/w/index.php?action=history&amp;feed=atom&amp;title=Calcul_vectorial"/> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;action=history"/> <updated>2024-12-01T03:27:40Z</updated> <subtitle>Istoricul versiunilor pentru această pagină din wiki</subtitle> <generator>MediaWiki 1.44.0-wmf.5</generator> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=30783&amp;oldid=prev</id> <title>Strainu: Robot: Înlocuiesc diacritice pentru corectarea diacriticelor</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=30783&amp;oldid=prev"/> <updated>2015-12-12T20:22:06Z</updated> <summary type="html">&lt;p&gt;Robot: Înlocuiesc diacritice pentru &lt;a href=&quot;https://en.wikipedia.org/wiki/corectarea_diacriticelor&quot; class=&quot;extiw&quot; title=&quot;wikipedia:corectarea diacriticelor&quot;&gt;corectarea diacriticelor&lt;/a&gt;&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 12 decembrie 2015 20:22&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Calculul vectorial''' este un domeniu al matematicii care se ocupă cu studiul &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;operaţiilor&lt;/del&gt; cu vectori și &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;aplicaţiile&lt;/del&gt; acestora în geometrie, fizică și în alte domenii.&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Calculul vectorial''' este un domeniu al matematicii care se ocupă cu studiul &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;operațiilor&lt;/ins&gt; cu vectori și &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;aplicațiile&lt;/ins&gt; acestora în geometrie, fizică și în alte domenii.&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Cuprins ==&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Cuprins ==&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt;</summary> <author><name>Strainu</name></author> </entry> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29615&amp;oldid=prev</id> <title>Nicolae Coman: completări (corectat automat)</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29615&amp;oldid=prev"/> <updated>2015-11-06T07:20:19Z</updated> <summary type="html">&lt;p&gt;completări (&lt;a href=&quot;/w/index.php?title=WP:DVN&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:DVN (pagină inexistentă)&quot;&gt;corectat automat&lt;/a&gt;)&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 6 noiembrie 2015 07:20&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Calculul vectorial''' este un domeniu al matematicii care se ocupă cu studiul operaţiilor cu vectori &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;şi&lt;/del&gt; aplicaţiile acestora în geometrie, fizică &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;şi&lt;/del&gt; în alte domenii.&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Calculul vectorial''' este un domeniu al matematicii care se ocupă cu studiul operaţiilor cu vectori &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;și&lt;/ins&gt; aplicaţiile acestora în geometrie, fizică &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;și&lt;/ins&gt; în alte domenii.&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Cuprins ==&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Cuprins ==&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 5:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 5:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_scalar|Produs scalar]]&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_scalar|Produs scalar]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_vectorial|Produs vectorial]]&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_vectorial|Produs vectorial]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Coordonate_cilindrice_și_sferice|Coordonate cilindrice și sferice]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Categorie:Matematică]]&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Categorie:Matematică]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt;</summary> <author><name>Nicolae Coman</name></author> </entry> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29611&amp;oldid=prev</id> <title>Nicolae Coman: categ</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29611&amp;oldid=prev"/> <updated>2015-11-05T14:35:19Z</updated> <summary type="html">&lt;p&gt;categ&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 5 noiembrie 2015 14:35&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 5:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 5:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_scalar|Produs scalar]]&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_scalar|Produs scalar]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_vectorial|Produs vectorial]]&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_vectorial|Produs vectorial]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Categorie:Matematică]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt;</summary> <author><name>Nicolae Coman</name></author> </entry> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29609&amp;oldid=prev</id> <title>Nicolae Coman: completări (corectat automat)</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29609&amp;oldid=prev"/> <updated>2015-11-05T14:31:36Z</updated> <summary type="html">&lt;p&gt;completări (&lt;a href=&quot;/w/index.php?title=WP:DVN&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:DVN (pagină inexistentă)&quot;&gt;corectat automat&lt;/a&gt;)&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 5 noiembrie 2015 14:31&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 4:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 4:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Vectori|Vectori]]&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Vectori|Vectori]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_scalar|Produs scalar]]&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_scalar|Produs scalar]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_vectorial|Produs vectorial]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;!-- diff cache key rowikibooks:diff:1.41:old-29608:rev-29609:wikidiff2=table:1.14.1:ff290eae --&gt; &lt;/table&gt;</summary> <author><name>Nicolae Coman</name></author> </entry> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29608&amp;oldid=prev</id> <title>Nicolae Coman: mutare conţinut şi creare cuprins</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29608&amp;oldid=prev"/> <updated>2015-11-05T14:30:10Z</updated> <summary type="html">&lt;p&gt;mutare conţinut şi creare cuprins&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 5 noiembrie 2015 14:30&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Fișier:Coord system CA 0.svg|thumb|right|250px|Reprezentarea grafică a unui punct de coordonate &amp;lt;math&amp;gt; x,y,z &amp;lt;/math&amp;gt;]]&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Calculul vectorial''' este un domeniu al matematicii care se ocupă cu studiul operaţiilor cu vectori şi aplicaţiile acestora în geometrie, fizică şi în alte domenii.&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Calculul vectorial''' este un domeniu al matematicii care se ocupă cu studiul operaţiilor cu vectori şi aplicaţiile acestora în geometrie, fizică şi în alte domenii.&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Cuprins ==&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Un punct &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; din plan poate fi reprezentat printr-o pereche de numere reale &amp;lt;math&amp;gt;(a_1, a_2),&amp;lt;/math&amp;gt; unde &amp;lt;math&amp;gt;a_1, a_2&amp;lt;/math&amp;gt; sunt '''coordonatele carteziene''' ale lui &amp;lt;math&amp;gt;P.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Vectori|Vectori]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [[Calcul vectorial/Produs_scalar|Produs scalar]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dacă &amp;lt;math&amp;gt;O&amp;lt;/math&amp;gt; este originea axelor de coordonate &amp;lt;math&amp;gt;Ox, \; Oy&amp;lt;/math&amp;gt;, &amp;lt;math&amp;gt;a_1, \; a_2&amp;lt;/math&amp;gt; se mai numesc şi componentele vectorului &amp;lt;math&amp;gt;\overrightarrow {OP}.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Se mai notează şi &amp;lt;math&amp;gt;a_1=x, \; a_2=y&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;În spaţiu, în locul expresiei &quot;''punctul'' &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; ''de coordonate'' &amp;lt;math&amp;gt;a_1, a_2, a_3&amp;lt;/math&amp;gt;&quot; se va spune mai simplu &quot;''punctul'' &amp;lt;math&amp;gt;a_1, a_2, a_3.&amp;lt;/math&amp;gt;&quot;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;a_1&amp;lt;/math&amp;gt; se mai numeşte şi coordonata x, &amp;lt;math&amp;gt;a_2&amp;lt;/math&amp;gt; coordonata y, iar &amp;lt;math&amp;gt;a_3&amp;lt;/math&amp;gt; coordonata z.&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Se va nota prin &amp;lt;math&amp;gt;\mathbb R^n&amp;lt;/math&amp;gt; mulţimea ''n''-uplurilor &amp;lt;math&amp;gt;(x_1, x_2, \cdots , x_n)&amp;lt;/math&amp;gt; cu &amp;lt;math&amp;gt;x_i \in \mathbb R, \; \forall i=\overline {1, n}.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Adunarea vectorilor şi înmulţirea acestora cu scalari ==&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Operaţia de adunare poate fi extinsă de pe &amp;lt;math&amp;gt;\mathbb R&amp;lt;/math&amp;gt; pe &amp;lt;math&amp;gt;\mathbb R^2&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;\mathbb R^3.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Astfel, pe &amp;lt;math&amp;gt;\mathbb R^3&amp;lt;/math&amp;gt; se defineşte suma tripletelor &amp;lt;math&amp;gt;(a_1, a_2, a_3)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;(b_1, b_2, b_3)&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;(a_1, a_2, a_3) + (b_1, b_2, b_3) = (a_1+b_1, a_2+b_2, a_3+b_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Elementul &amp;lt;math&amp;gt;(0,0,0)&amp;lt;/math&amp;gt; este numit '''elementul zero''' (sau chiar '''zero''') al lui &amp;lt;math&amp;gt;\mathbb R^3.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dându-se punctul &amp;lt;math&amp;gt;(a_1, a_2, a_3),&amp;lt;/math&amp;gt; elementul &amp;lt;math&amp;gt;(-a_1, -a_2, -a_3)&amp;lt;/math&amp;gt; este numit '''inversul''' sau '''negativul''' şi se poate scrie:&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;(a_1, a_2, a_3) + (-b_1, -b_2, -b_3) \overset {def}{=} (a_1, a_2, a_3) - (b_1, b_2, b_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Un vector adunat cu inversul acestuia ne dau zero:&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;(a_1, a_2, a_3) + (-a_1, -a_2, -a_3)=(0,0,0).&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;O altă operaţie pe &amp;lt;math&amp;gt;\mathbb R^3&amp;lt;/math&amp;gt; este ''înmulţirea unui vector cu un scalar'', unde prin scalar se înţelege număr real.&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Astfel, dându-se un scalar &amp;lt;math&amp;gt;\alpha \in \mathbb R&amp;lt;/math&amp;gt; şi un vector &amp;lt;math&amp;gt;(a_1, a_2, a_3) \in \mathbb R^3,&amp;lt;/math&amp;gt; se defineşte '''produsul scalar''' prin:&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;\alpha \cdot (a_1, a_2, a_3) \overset {def}{=} (\alpha \cdot a_1, \alpha \cdot a_2, \alpha \cdot a_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Adunarea şi înmulţirea cu scalari a vectorilor din &amp;lt;math&amp;gt;\mathbb R^3&amp;lt;/math&amp;gt; satisfac proprietăţile:&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(i) &amp;amp;nbsp; &amp;lt;math&amp;gt; \; (\alpha \beta) (a_1, a_2, a_3) = \alpha [\beta (a_1, a_2, a_3)]&amp;lt;/math&amp;gt; (asociativitate)&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(ii) &amp;amp;nbsp; &amp;lt;math&amp;gt; \; (\alpha + \beta) (a_1, a_2, a_3) = \alpha (a_1, a_2, a_3) + \beta (a_1, a_2, a_3)]&amp;lt;/math&amp;gt; (distributivitate)&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(iii) &amp;amp;nbsp; &amp;lt;math&amp;gt; \; \alpha [(a_1, a_2, a_3) + (b_1, b_2, b_3)]= \alpha (a_1, a_2, a_3) + \alpha (b_1, b_2, b_3)]&amp;lt;/math&amp;gt; (distributivitate)&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(iv) &amp;amp;nbsp; &amp;lt;math&amp;gt; \alpha \cdot (0,0,0) = (0,0,0) &amp;lt;/math&amp;gt; (element nul)&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(v) &amp;amp;nbsp; &amp;lt;math&amp;gt; 0 \cdot (a_1, a_2,a_3) = (0,0,0) &amp;lt;/math&amp;gt; (element nul)&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(vi) &amp;amp;nbsp; &amp;lt;math&amp;gt; 1 \cdot (a_1, a_2,a_3) = (a_1, a_2,a_3). &amp;lt;/math&amp;gt; (element unitate)&lt;/div&gt;&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-added&quot;&gt;&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt;</summary> <author><name>Nicolae Coman</name></author> </entry> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29605&amp;oldid=prev</id> <title>Nicolae Coman: introducere imagine</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29605&amp;oldid=prev"/> <updated>2015-11-05T11:18:01Z</updated> <summary type="html">&lt;p&gt;introducere imagine&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 5 noiembrie 2015 11:18&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Fișier:Coord system CA 0.svg|thumb|right|250px|Reprezentarea grafică a unui punct de coordonate &amp;lt;math&amp;gt; x,y,z &amp;lt;/math&amp;gt;]]&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Calculul vectorial''' este un domeniu al matematicii care se ocupă cu studiul operaţiilor cu vectori şi aplicaţiile acestora în geometrie, fizică şi în alte domenii.&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Calculul vectorial''' este un domeniu al matematicii care se ocupă cu studiul operaţiilor cu vectori şi aplicaţiile acestora în geometrie, fizică şi în alte domenii.&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt;</summary> <author><name>Nicolae Coman</name></author> </entry> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29604&amp;oldid=prev</id> <title>Nicolae Coman: continuare editare (corectat automat)</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29604&amp;oldid=prev"/> <updated>2015-11-05T11:12:28Z</updated> <summary type="html">&lt;p&gt;continuare editare (&lt;a href=&quot;/w/index.php?title=WP:DVN&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:DVN (pagină inexistentă)&quot;&gt;corectat automat&lt;/a&gt;)&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 5 noiembrie 2015 11:12&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 30:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 30:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;\alpha \cdot (a_1, a_2, a_3) \overset {def}{=} (\alpha \cdot a_1, \alpha \cdot a_2, \alpha \cdot a_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;\alpha \cdot (a_1, a_2, a_3) \overset {def}{=} (\alpha \cdot a_1, \alpha \cdot a_2, \alpha \cdot a_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Adunarea şi înmulţirea cu scalari a vectorilor din &amp;lt;math&amp;gt;\mathbb R^3&amp;lt;/math&amp;gt; satisfac proprietăţile:&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(i) &amp;amp;nbsp; &amp;lt;math&amp;gt; \; (\alpha \beta) (a_1, a_2, a_3) = \alpha [\beta (a_1, a_2, a_3)]&amp;lt;/math&amp;gt; (asociativitate)&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(ii) &amp;amp;nbsp; &amp;lt;math&amp;gt; \; (\alpha + \beta) (a_1, a_2, a_3) = \alpha (a_1, a_2, a_3) + \beta (a_1, a_2, a_3)]&amp;lt;/math&amp;gt; (distributivitate)&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(iii) &amp;amp;nbsp; &amp;lt;math&amp;gt; \; \alpha [(a_1, a_2, a_3) + (b_1, b_2, b_3)]= \alpha (a_1, a_2, a_3) + \alpha (b_1, b_2, b_3)]&amp;lt;/math&amp;gt; (distributivitate)&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(iv) &amp;amp;nbsp; &amp;lt;math&amp;gt; \alpha \cdot (0,0,0) = (0,0,0) &amp;lt;/math&amp;gt; (element nul)&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(v) &amp;amp;nbsp; &amp;lt;math&amp;gt; 0 \cdot (a_1, a_2,a_3) = (0,0,0) &amp;lt;/math&amp;gt; (element nul)&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;(vi) &amp;amp;nbsp; &amp;lt;math&amp;gt; 1 \cdot (a_1, a_2,a_3) = (a_1, a_2,a_3). &amp;lt;/math&amp;gt; (element unitate)&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt;</summary> <author><name>Nicolae Coman</name></author> </entry> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29603&amp;oldid=prev</id> <title>Nicolae Coman: continuare editare (corectat automat)</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29603&amp;oldid=prev"/> <updated>2015-11-05T11:10:56Z</updated> <summary type="html">&lt;p&gt;continuare editare (&lt;a href=&quot;/w/index.php?title=WP:DVN&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:DVN (pagină inexistentă)&quot;&gt;corectat automat&lt;/a&gt;)&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 5 noiembrie 2015 11:10&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 21:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 21:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;(a_1, a_2, a_3) + (-b_1, -b_2, -b_3) \overset {def}{=} (a_1, a_2, a_3) - (b_1, b_2, b_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;(a_1, a_2, a_3) + (-b_1, -b_2, -b_3) \overset {def}{=} (a_1, a_2, a_3) - (b_1, b_2, b_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Un vector adunat cu inversul acestuia ne dau zero:&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;(a_1, a_2, a_3) + (-a_1, -a_2, -a_3)=(0,0,0).&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;O altă operaţie pe &amp;lt;math&amp;gt;\mathbb R^3&amp;lt;/math&amp;gt; este ''înmulţirea unui vector cu un scalar'', unde prin scalar se înţelege număr real.&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Astfel, dându-se un scalar &amp;lt;math&amp;gt;\alpha \in \mathbb R&amp;lt;/math&amp;gt; şi un vector &amp;lt;math&amp;gt;(a_1, a_2, a_3) \in \mathbb R^3,&amp;lt;/math&amp;gt; se defineşte '''produsul scalar''' prin:&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;\alpha \cdot (a_1, a_2, a_3) \overset {def}{=} (\alpha \cdot a_1, \alpha \cdot a_2, \alpha \cdot a_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;/table&gt;</summary> <author><name>Nicolae Coman</name></author> </entry> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29602&amp;oldid=prev</id> <title>Nicolae Coman: introducere capitol nou (corectat automat)</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29602&amp;oldid=prev"/> <updated>2015-11-05T11:09:53Z</updated> <summary type="html">&lt;p&gt;introducere capitol nou (&lt;a href=&quot;/w/index.php?title=WP:DVN&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:DVN (pagină inexistentă)&quot;&gt;corectat automat&lt;/a&gt;)&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 5 noiembrie 2015 11:09&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 10:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 10:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Se va nota prin &amp;lt;math&amp;gt;\mathbb R^n&amp;lt;/math&amp;gt; mulţimea ''n''-uplurilor &amp;lt;math&amp;gt;(x_1, x_2, \cdots , x_n)&amp;lt;/math&amp;gt; cu &amp;lt;math&amp;gt;x_i \in \mathbb R, \; \forall i=\overline {1, n}.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Se va nota prin &amp;lt;math&amp;gt;\mathbb R^n&amp;lt;/math&amp;gt; mulţimea ''n''-uplurilor &amp;lt;math&amp;gt;(x_1, x_2, \cdots , x_n)&amp;lt;/math&amp;gt; cu &amp;lt;math&amp;gt;x_i \in \mathbb R, \; \forall i=\overline {1, n}.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Adunarea vectorilor şi înmulţirea acestora cu scalari ==&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Operaţia de adunare poate fi extinsă de pe &amp;lt;math&amp;gt;\mathbb R&amp;lt;/math&amp;gt; pe &amp;lt;math&amp;gt;\mathbb R^2&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;\mathbb R^3.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Astfel, pe &amp;lt;math&amp;gt;\mathbb R^3&amp;lt;/math&amp;gt; se defineşte suma tripletelor &amp;lt;math&amp;gt;(a_1, a_2, a_3)&amp;lt;/math&amp;gt; şi &amp;lt;math&amp;gt;(b_1, b_2, b_3)&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;(a_1, a_2, a_3) + (b_1, b_2, b_3) = (a_1+b_1, a_2+b_2, a_3+b_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Elementul &amp;lt;math&amp;gt;(0,0,0)&amp;lt;/math&amp;gt; este numit '''elementul zero''' (sau chiar '''zero''') al lui &amp;lt;math&amp;gt;\mathbb R^3.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Dându-se punctul &amp;lt;math&amp;gt;(a_1, a_2, a_3),&amp;lt;/math&amp;gt; elementul &amp;lt;math&amp;gt;(-a_1, -a_2, -a_3)&amp;lt;/math&amp;gt; este numit '''inversul''' sau '''negativul''' şi se poate scrie:&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;::&amp;lt;math&amp;gt;(a_1, a_2, a_3) + (-b_1, -b_2, -b_3) \overset {def}{=} (a_1, a_2, a_3) - (b_1, b_2, b_3). &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;!-- diff cache key rowikibooks:diff:1.41:old-29600:rev-29602:wikidiff2=table:1.14.1:ff290eae --&gt; &lt;/table&gt;</summary> <author><name>Nicolae Coman</name></author> </entry> <entry> <id>https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29600&amp;oldid=prev</id> <title>Nicolae Coman: completări (corectat automat)</title> <link rel="alternate" type="text/html" href="https://ro.wikibooks.org/w/index.php?title=Calcul_vectorial&amp;diff=29600&amp;oldid=prev"/> <updated>2015-11-05T11:07:40Z</updated> <summary type="html">&lt;p&gt;completări (&lt;a href=&quot;/w/index.php?title=WP:DVN&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:DVN (pagină inexistentă)&quot;&gt;corectat automat&lt;/a&gt;)&lt;/p&gt; &lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;col class=&quot;diff-marker&quot; /&gt; &lt;col class=&quot;diff-content&quot; /&gt; &lt;tr class=&quot;diff-title&quot; lang=&quot;ro&quot;&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Versiunea anterioară&lt;/td&gt; &lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Versiunea de la data 5 noiembrie 2015 11:07&lt;/td&gt; &lt;/tr&gt;&lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Linia 1:&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Calculul vectorial''' este un domeniu al matematicii care se ocupă cu studiul operaţiilor cu vectori şi aplicaţiile acestora în geometrie, fizică şi în alte domenii.&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt; &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Un punct &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; din plan poate fi reprezentat printr-o pereche de numere reale &amp;lt;math&amp;gt;(a_1, a_2),&amp;lt;/math&amp;gt; unde &amp;lt;math&amp;gt;a_1, a_2&amp;lt;/math&amp;gt; sunt '''coordonatele carteziene''' ale lui &amp;lt;math&amp;gt;P.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Un punct &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; din plan poate fi reprezentat printr-o pereche de numere reale &amp;lt;math&amp;gt;(a_1, a_2),&amp;lt;/math&amp;gt; unde &amp;lt;math&amp;gt;a_1, a_2&amp;lt;/math&amp;gt; sunt '''coordonatele carteziene''' ale lui &amp;lt;math&amp;gt;P.&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt; &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt; &lt;/tr&gt; &lt;!-- diff cache key rowikibooks:diff:1.41:old-29599:rev-29600:wikidiff2=table:1.14.1:ff290eae --&gt; &lt;/table&gt;</summary> <author><name>Nicolae Coman</name></author> </entry> </feed>