Punkte und Vektoren

Version 5.1 von martina am 2023/05/19 12:46

Warnung: Aus Sicherheitsgründen wird das Dokument in einem eingeschränkten Modus angezeigt, da es sich nicht um die aktuelle Version handelt. Dadurch kann es zu Abweichungen und Fehlern kommen.

Contents

Punkte im Raum
Vektoren

Kompetenzen

K5 Ich kann Vektoren als Pfeilklassen deuten
K5, K4 Ich kann Vektoren geometrisch als Verschiebung interpretieren
K4 Ich kann geometrische Objekte im dreidimensionalen Koordinatensystem zeichnen
K4, K5 Ich kann das Koordinatensystem nutzen, um geometrische Sachverhalte zu beschreiben

Punkte im Raum

Das Makro [aufgabe] konnte nicht ausgeführt werden. Grund: [Parameter [afb] is mandatory]. Klicke auf diese Nachricht, um Details zu erfahren.

org.xwiki.rendering.macro.parameter.MacroParameterException: Parameter [afb] is mandatory
at org.xwiki.rendering.wikimacro.internal.DefaultWikiMacro.validate(DefaultWikiMacro.java:134)
at org.xwiki.rendering.wikimacro.internal.DefaultWikiMacro.execute(DefaultWikiMacro.java:98)
at org.xwiki.rendering.wikimacro.internal.DefaultWikiMacro.execute(DefaultWikiMacro.java:53)
at org.xwiki.rendering.internal.transformation.macro.MacroTransformation.transform(MacroTransformation.java:311)
at org.xwiki.rendering.internal.transformation.DefaultRenderingContext.transformInContext(DefaultRenderingContext.java:183)
at org.xwiki.rendering.internal.transformation.DefaultTransformationManager.performTransformations(DefaultTransformationManager.java:88)
at org.xwiki.display.internal.DocumentContentAsyncExecutor.executeInCurrentExecutionContext(DocumentContentAsyncExecutor.java:396)
at org.xwiki.display.internal.DocumentContentAsyncExecutor.execute(DocumentContentAsyncExecutor.java:269)
at org.xwiki.display.internal.DocumentContentAsyncRenderer.execute(DocumentContentAsyncRenderer.java:112)
at org.xwiki.rendering.async.internal.block.AbstractBlockAsyncRenderer.render(AbstractBlockAsyncRenderer.java:157)
at org.xwiki.rendering.async.internal.block.AbstractBlockAsyncRenderer.render(AbstractBlockAsyncRenderer.java:54)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.syncRender(DefaultAsyncRendererExecutor.java:290)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.render(DefaultAsyncRendererExecutor.java:267)
at org.xwiki.rendering.async.internal.block.DefaultBlockAsyncRendererExecutor.execute(DefaultBlockAsyncRendererExecutor.java:125)
at org.xwiki.display.internal.DocumentContentDisplayer.display(DocumentContentDisplayer.java:67)
at org.xwiki.display.internal.DocumentContentDisplayer.display(DocumentContentDisplayer.java:43)
at org.xwiki.display.internal.DefaultDocumentDisplayer.display(DefaultDocumentDisplayer.java:96)
at org.xwiki.display.internal.DefaultDocumentDisplayer.display(DefaultDocumentDisplayer.java:39)
at org.xwiki.sheet.internal.SheetDocumentDisplayer.display(SheetDocumentDisplayer.java:123)
at org.xwiki.sheet.internal.SheetDocumentDisplayer.display(SheetDocumentDisplayer.java:52)
at org.xwiki.display.internal.ConfiguredDocumentDisplayer.display(ConfiguredDocumentDisplayer.java:68)
at org.xwiki.display.internal.ConfiguredDocumentDisplayer.display(ConfiguredDocumentDisplayer.java:42)
at com.xpn.xwiki.doc.XWikiDocument.display(XWikiDocument.java:1388)
at com.xpn.xwiki.doc.XWikiDocument.getRenderedContent(XWikiDocument.java:1524)
at com.xpn.xwiki.doc.XWikiDocument.displayDocument(XWikiDocument.java:1474)
at com.xpn.xwiki.doc.XWikiDocument.displayDocument(XWikiDocument.java:1443)
at com.xpn.xwiki.api.Document.displayDocument(Document.java:788)
at java.base/jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:104)
at java.base/java.lang.reflect.Method.invoke(Method.java:577)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.doInvoke(UberspectImpl.java:571)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.invoke(UberspectImpl.java:554)
at org.apache.velocity.runtime.parser.node.ASTMethod.execute(ASTMethod.java:221)
at org.apache.velocity.runtime.parser.node.ASTReference.execute(ASTReference.java:368)
at org.apache.velocity.runtime.parser.node.ASTReference.value(ASTReference.java:704)
at org.apache.velocity.runtime.parser.node.ASTExpression.value(ASTExpression.java:75)
at org.apache.velocity.runtime.parser.node.ASTSetDirective.render(ASTSetDirective.java:242)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.runtime.parser.node.ASTIfStatement.render(ASTIfStatement.java:190)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.xwiki.velocity.internal.directive.TryCatchDirective.render(TryCatchDirective.java:86)
at org.apache.velocity.runtime.parser.node.ASTDirective.render(ASTDirective.java:304)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.Template.merge(Template.java:358)
at org.apache.velocity.Template.merge(Template.java:262)
at org.xwiki.velocity.internal.InternalVelocityEngine.evaluate(InternalVelocityEngine.java:225)
at com.xpn.xwiki.internal.template.VelocityTemplateEvaluator.evaluateContent(VelocityTemplateEvaluator.java:105)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.evaluateContent(TemplateAsyncRenderer.java:219)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.renderVelocity(TemplateAsyncRenderer.java:174)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:135)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:54)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.lambda$syncRender$0(DefaultAsyncRendererExecutor.java:284)
at com.xpn.xwiki.internal.security.authorization.DefaultAuthorExecutor.call(DefaultAuthorExecutor.java:98)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.syncRender(DefaultAsyncRendererExecutor.java:284)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.render(DefaultAsyncRendererExecutor.java:267)
at org.xwiki.rendering.async.internal.block.DefaultBlockAsyncRendererExecutor.render(DefaultBlockAsyncRendererExecutor.java:154)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:904)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderFromSkin(InternalTemplateManager.java:866)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:853)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderNoException(InternalTemplateManager.java:808)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderNoException(InternalTemplateManager.java:800)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.renderNoException(DefaultTemplateManager.java:79)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.renderNoException(DefaultTemplateManager.java:73)
at org.xwiki.template.script.TemplateScriptService.render(TemplateScriptService.java:54)
at java.base/jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:104)
at java.base/java.lang.reflect.Method.invoke(Method.java:577)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.doInvoke(UberspectImpl.java:571)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.invoke(UberspectImpl.java:554)
at org.apache.velocity.runtime.parser.node.ASTMethod.execute(ASTMethod.java:221)
at org.apache.velocity.runtime.parser.node.ASTReference.execute(ASTReference.java:368)
at org.apache.velocity.runtime.parser.node.ASTReference.render(ASTReference.java:492)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.directive.VelocimacroProxy.render(VelocimacroProxy.java:218)
at org.apache.velocity.runtime.directive.RuntimeMacro.render(RuntimeMacro.java:331)
at org.apache.velocity.runtime.directive.RuntimeMacro.render(RuntimeMacro.java:261)
at org.apache.velocity.runtime.parser.node.ASTDirective.render(ASTDirective.java:304)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.Template.merge(Template.java:358)
at org.apache.velocity.Template.merge(Template.java:262)
at org.xwiki.velocity.internal.InternalVelocityEngine.evaluate(InternalVelocityEngine.java:225)
at com.xpn.xwiki.internal.template.VelocityTemplateEvaluator.evaluateContent(VelocityTemplateEvaluator.java:105)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.evaluateContent(TemplateAsyncRenderer.java:219)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.renderVelocity(TemplateAsyncRenderer.java:174)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:135)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:54)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.lambda$syncRender$0(DefaultAsyncRendererExecutor.java:284)
at com.xpn.xwiki.internal.security.authorization.DefaultAuthorExecutor.call(DefaultAuthorExecutor.java:98)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.syncRender(DefaultAsyncRendererExecutor.java:284)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.render(DefaultAsyncRendererExecutor.java:267)
at org.xwiki.rendering.async.internal.block.DefaultBlockAsyncRendererExecutor.render(DefaultBlockAsyncRendererExecutor.java:154)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:904)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderFromSkin(InternalTemplateManager.java:866)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:853)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderNoException(InternalTemplateManager.java:808)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderNoException(InternalTemplateManager.java:800)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.renderNoException(DefaultTemplateManager.java:79)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.renderNoException(DefaultTemplateManager.java:73)
at org.xwiki.template.script.TemplateScriptService.render(TemplateScriptService.java:54)
at java.base/jdk.internal.reflect.DirectMethodHandleAccessor.invoke(DirectMethodHandleAccessor.java:104)
at java.base/java.lang.reflect.Method.invoke(Method.java:577)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.doInvoke(UberspectImpl.java:571)
at org.apache.velocity.util.introspection.UberspectImpl$VelMethodImpl.invoke(UberspectImpl.java:554)
at org.apache.velocity.runtime.parser.node.ASTMethod.execute(ASTMethod.java:221)
at org.apache.velocity.runtime.parser.node.ASTReference.execute(ASTReference.java:368)
at org.apache.velocity.runtime.parser.node.ASTReference.render(ASTReference.java:492)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.directive.VelocimacroProxy.render(VelocimacroProxy.java:218)
at org.apache.velocity.runtime.directive.RuntimeMacro.render(RuntimeMacro.java:331)
at org.apache.velocity.runtime.directive.RuntimeMacro.render(RuntimeMacro.java:261)
at org.apache.velocity.runtime.parser.node.ASTDirective.render(ASTDirective.java:304)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.parser.node.ASTIfStatement.render(ASTIfStatement.java:171)
at org.apache.velocity.runtime.parser.node.ASTBlock.render(ASTBlock.java:147)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.runtime.parser.node.ASTIfStatement.render(ASTIfStatement.java:190)
at org.apache.velocity.runtime.parser.node.SimpleNode.render(SimpleNode.java:439)
at org.apache.velocity.Template.merge(Template.java:358)
at org.apache.velocity.Template.merge(Template.java:262)
at org.xwiki.velocity.internal.InternalVelocityEngine.evaluate(InternalVelocityEngine.java:225)
at com.xpn.xwiki.internal.template.VelocityTemplateEvaluator.evaluateContent(VelocityTemplateEvaluator.java:105)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.evaluateContent(TemplateAsyncRenderer.java:219)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.renderVelocity(TemplateAsyncRenderer.java:174)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:135)
at com.xpn.xwiki.internal.template.TemplateAsyncRenderer.render(TemplateAsyncRenderer.java:54)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.lambda$syncRender$0(DefaultAsyncRendererExecutor.java:284)
at com.xpn.xwiki.internal.security.authorization.DefaultAuthorExecutor.call(DefaultAuthorExecutor.java:98)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.syncRender(DefaultAsyncRendererExecutor.java:284)
at org.xwiki.rendering.async.internal.DefaultAsyncRendererExecutor.render(DefaultAsyncRendererExecutor.java:267)
at org.xwiki.rendering.async.internal.block.DefaultBlockAsyncRendererExecutor.render(DefaultBlockAsyncRendererExecutor.java:154)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:904)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderFromSkin(InternalTemplateManager.java:866)
at com.xpn.xwiki.internal.template.InternalTemplateManager.renderFromSkin(InternalTemplateManager.java:846)
at com.xpn.xwiki.internal.template.InternalTemplateManager.render(InternalTemplateManager.java:832)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.render(DefaultTemplateManager.java:91)
at com.xpn.xwiki.internal.template.DefaultTemplateManager.render(DefaultTemplateManager.java:85)
at com.xpn.xwiki.XWiki.evaluateTemplate(XWiki.java:2564)
at com.xpn.xwiki.web.Utils.parseTemplate(Utils.java:180)
at com.xpn.xwiki.web.XWikiAction.execute(XWikiAction.java:651)
at com.xpn.xwiki.web.XWikiAction.execute(XWikiAction.java:339)
at com.xpn.xwiki.web.LegacyActionServlet.service(LegacyActionServlet.java:108)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:764)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:227)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at com.xpn.xwiki.web.ActionFilter.doFilter(ActionFilter.java:122)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.wysiwyg.filter.ConversionFilter.doFilter(ConversionFilter.java:61)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:53)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.container.servlet.filters.internal.SetHTTPHeaderFilter.doFilter(SetHTTPHeaderFilter.java:63)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.resource.servlet.RoutingFilter.doFilter(RoutingFilter.java:132)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.container.servlet.filters.internal.SavedRequestRestorerFilter.doFilter(SavedRequestRestorerFilter.java:208)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.xwiki.container.servlet.filters.internal.SetCharacterEncodingFilter.doFilter(SetCharacterEncodingFilter.java:117)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:189)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:162)
at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:197)
at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:97)
at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:540)
at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:135)
at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:92)
at org.apache.catalina.valves.AbstractAccessLogValve.invoke(AbstractAccessLogValve.java:687)
at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:78)
at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:359)
at org.apache.coyote.ajp.AjpProcessor.service(AjpProcessor.java:433)
at org.apache.coyote.AbstractProcessorLight.process(AbstractProcessorLight.java:65)
at org.apache.coyote.AbstractProtocol$ConnectionHandler.process(AbstractProtocol.java:889)
at org.apache.tomcat.util.net.NioEndpoint$SocketProcessor.doRun(NioEndpoint.java:1735)
at org.apache.tomcat.util.net.SocketProcessorBase.run(SocketProcessorBase.java:49)
at org.apache.tomcat.util.threads.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1191)
at org.apache.tomcat.util.threads.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:659)
at org.apache.tomcat.util.threads.TaskThread$WrappingRunnable.run(TaskThread.java:61)
at java.base/java.lang.Thread.run(Thread.java:833)

a) Geben Sie an, in welcher Koordinatenebene der Punkt A(2|1|0) liegt.
b) Nennen Sie einen Punkt, der auf der x_1 -Achse liegt.

Unbekanntes Makro: tags. Klicke auf diese Nachricht, um Details zu erfahren.

Das Makro [aufgabe] konnte nicht ausgeführt werden. Grund: [Parameter [afb] is mandatory]. Klicke auf diese Nachricht, um Details zu erfahren.

Ein Architekt plant ein modernes Museum. Im Modell hat das Museum eine rechteckige Grundfläche mit den Eckpunkten A_1(0|0|0) , B_1(10|0|0) , C_1(10|5|0) und D_1(0|5|0) .

Und ein Dach, dass aus den vier Eckpunkten: A_2(0|0|2) , B_2(10|0|2) , C_2(10|6|2) und
$D_2(0|5{,}5|2{,}5)$ gebildet wird.

Die von der Grundfläche zum Dach verlaufenden Kanten des Modells verbinden Punkte gleichen Buchstabens, z. B. Ist A_1 mit A_2 verbunden. 1 cm im Modell entspricht 10 m.

Zeichnen Sie das Modell in ein geeignetes Koordinatensystem.

Unbekanntes Makro: tags. Klicke auf diese Nachricht, um Details zu erfahren.

Vektoren

Das Makro [aufgabe] konnte nicht ausgeführt werden. Grund: [Parameter [afb] is mandatory]. Klicke auf diese Nachricht, um Details zu erfahren.

Betrachtet wird die Pyramide ABCS . Ihre Grundfläche ist das rechtwinklige Dreieck ABC ; die Hypotenuse $\overline{AB}$ ist 5 cm lang, die Kathete $\overline{AC}$ 4 cm. Die Kante $\overline{CS}$ steht senkrecht zur Grundfläche und hat eine Länge von 7 cm.

Die Pyramide soll in einem Koordinatensystem dargestellt werden, in dem eine Längeneinheit 1 cm entspricht. Geben Sie mögliche Koordinaten der Eckpunkte der Pyramide an!

Unbekanntes Makro: tags. Klicke auf diese Nachricht, um Details zu erfahren.

Punkte und Vektoren

Kompetenzen

Punkte im Raum

Vektoren

Hauptnavigation

Suchen

Zuletzt besucht

Zuletzt geändert

unfertig	fertig
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