{"questions":[{"params":{"answers":[{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\$\\cos \\alpha = \\frac{|\\vec{a}\\cdot\\vec{n}|}{|\\vec{a}|\\cdot|\\vec{n}|}\$<\/span><\/div>"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\$\\sin \\alpha = \\frac{|\\vec{a}\\cdot\\vec{n}|}{|\\vec{a}|\\cdot|\\vec{n}|}\$<\/span><\/div>"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\$\\cos \\alpha = \\frac{\\vec{a}\\cdot\\vec{n}}{|\\vec{a}|\\cdot|\\vec{n}|}\$<\/span><\/div>"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\$\\sin \\alpha = \\frac{\\vec{a}\\cdot\\vec{n}}{|\\vec{a}|\\cdot|\\vec{n}|}\$<\/span><\/div>"}],"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Tipp anzeigen","scoreBarLabel":"Score","tipAvailable":"Tipp verf\u00fcgbar","feedbackAvailable":"Feedback verf\u00fcgbar","readFeedback":"Feedback lesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Korrekte Antwort","shouldCheck":"H\u00e4tte ausgew\u00e4hlt werden sollen","shouldNotCheck":"H\u00e4tte nicht ausgew\u00e4hlt werden sollen","noInput":"Please answer before viewing the solution"},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

Wie kann der Schnittwinkel \$\\alpha\$<\/span>\u00a0von einer Geraden mit dem Richtungsvektor \$\\vec{a}\$<\/span>\u00a0und einer Ebene mit dem Normalenvektor \$\\vec{n}\$<\/span> berechnet werden?<\/div>","media":{},"type":"multi","overallFeedback":[{"from":0,"to":100,"feedback":""}],"difficultyLevel":"","behaviour":{"enableRetry":false,"enableSolutionsButton":false,"randomAnswers":true,"autoCheck":false}},"library":"H5P.MultiChoice 1.10","subContentId":"0177ba59-46e0-4485-9446-580f08e0cb0a"},{"params":{"text":"

Gegeben sind eine Gerade \$g\$<\/span>\u00a0mit dem Richtungsvektor \$\\vec{a}=\\left(\\begin{array}{c}2\\\\3\\\\1\\end{array}\\right)\$<\/span>\u00a0und eine Ebene \$E\$<\/span>\u00a0mit dem Normalenvektor \$\\vec{n}=\\left(\\begin{array}{c}3\\\\-1\\\\4\\end{array}\\right)\$<\/span>.<\/p>

Wie gro\u00df ist der Neigungswinkel (Schnittwinkel) zwischen der Geraden und der Ebene?<\/p>

Hinweis: Gib das Ergebnis auf eine Nachkommastelle gerundet, in Ziffern und ohne Einheit an (z. B. 12,7).<\/p><\/div>","showSolutions":"L\u00f6sung","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte alle Leerzeichen ausf\u00fcllen.","answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","behaviour":{"acceptSpellingErrors":false,"assistiveKeyboard":"none","enableRetry":false,"enableSolutionsButton":false,"autoCheck":false,"showSolutionsRequiresInput":false,"keyboardOptions":[]},"confirmCheck":{"header":"Beenden?","body":"Soll wirklich beendet werden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Wirklich nochmal versuchen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

Antwort<\/div>

*21,5*<\/div>"],"media":{},"overallFeedback":[{"from":0,"to":100,"feedback":""}],"difficultyLevel":""},"library":"H5P.Blanks 1.8","subContentId":"b4b019f5-afba-456d-960f-057a019ed3e3"},{"params":{"answers":[{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\$11,35\u00b0\$<\/span><\/div>"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\$73,87\u00b0\$<\/span><\/div>"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\$94,39\u00b0\$<\/span><\/div>"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"

\$45,25\u00b0\$<\/span><\/div>"}],"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Tipp anzeigen","scoreBarLabel":"Score","tipAvailable":"Tipp verf\u00fcgbar","feedbackAvailable":"Feedback verf\u00fcgbar","readFeedback":"Feedback lesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Korrekte Antwort","shouldCheck":"H\u00e4tte ausgew\u00e4hlt werden sollen","shouldNotCheck":"H\u00e4tte nicht ausgew\u00e4hlt werden sollen","noInput":"Please answer before viewing the solution"},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"

Gegeben sei eine Gerade \$g\$<\/span> mit dem Richtungsvektor \$\\begin{pmatrix} 2\\\\ 2\\\\ 3\\\\ \\end{pmatrix}\$<\/span>\u00a0und die Ebene \$E: 3x+2y-5z=12\$<\/span>\u200b.<\/p>

\u00a0<\/p>

Bestimmen Sie den Neigungswinkel der Geraden \$g\$<\/span> zu der Ebene \$E\$<\/span>.<\/p><\/div>","media":{},"type":"multi","overallFeedback":[{"from":0,"to":100,"feedback":""}],"difficultyLevel":"","behaviour":{"enableRetry":false,"enableSolutionsButton":false,"randomAnswers":true,"autoCheck":false}},"library":"H5P.MultiChoice 1.10","subContentId":"4a4c5926-b598-49b7-bf95-49008d7290dc"}],"passPercentage":60,"questionSetTitle":"Neigungswinkel einer Geraden zu einer Ebene bestimmen (einfach)","override":{"showSolutionButton":null,"retryButton":null,"globalFeedback":[{"from":0,"to":19,"feedback":"Es ist noch kein Meister vom Himmel gefallen. Schau dir noch einmal das Lernvideo oder die Schritt-f\u00fcr-Schritt-Anleitungen zum Thema an."},{"from":20,"to":49,"feedback":"\u00dcbung macht den Meister! Wiederhole das Lernvideo oder lies dir die Schritt-f\u00fcr-Schritt-Anleitung durch. Versuche es noch einmal."},{"from":50,"to":69,"feedback":"Du kennst dich schon gut im Thema aus. Weiter so!"},{"from":70,"to":99,"feedback":"Wow! Fast alles richtig gemacht."},{"from":100,"to":100,"feedback":"Herzlichen Gl\u00fcckwunsch! Du hast alle Aufgaben richtig gel\u00f6st."}],"instantSolution":true,"tutor":"

\n \n $\"Tutor$ \n\n\n\n \n\n \n<\/div>\n"},"randomQuestions":false,"texts":{"answeredText":"Beantwortet","currentQuestionText":"Aktuelle Frage","finishButton":"zur Abschlussseite","dotProgressHint":"Anzahl der Fragen in dieser \u00dcbung","jumpToQuestion":"Gehe zu Frage @current von @total","nextButton":"Weiter","prevButton":"Zur\u00fcck","questionLabel":"Frage","readSpeakerProgress":"Frage @current von @total","textualProgress":"Frage @current von @total Fragen","unansweredText":"Unbeantwortet"},"endGame":{"greetingMessage":"Dein Ergebnis!","message":"Du hast @score Punkt von @total m\u00f6glichen.","messagePlural":"Du hast @score Punkte von @total m\u00f6glichen.","finishButtonText":"zur Abschlussseite","solutionButtonText":"L\u00f6sungen anzeigen","retryButtonText":"Nochmal versuchen","skipButtonText":"Video \u00fcberspringen","showSolutionButton":true,"showRetryButton":true,"showRecommendedAsset":false,"recommendedAsset":null}}

Lernjahr 1

Wie du den Neigungswinkel einer Geraden zu einer Ebene bestimmst

Neigungswinkel einer Geraden zu einer Ebene bestimmen

Lernjahr 1