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The vector \\(t\\vec{v}\\) always shares the same direction with \\(\\vec{v}\\). <\/p>\n"},"subContentId":"ce406099-50b3-499c-b3a5-efba304a847f","metadata":{"contentType":"True\/False Question","license":"U","title":"scalar multiple of a vector"}},"pause":true,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""},{"x":17.400881057268723,"y":50.29354207436399,"width":10,"height":10,"duration":{"from":94.239,"to":104.239},"libraryTitle":"Statements","action":{"library":"H5P.Summary 1.10","params":{"intro":"Choose the correct statement.","summaries":[{"subContentId":"d7ea3900-2ca9-4fcb-8814-47afc493202b","summary":["

It's a straight line. <\/p>\n","

They are all parallel. <\/p>\n","

They are random. <\/p>\n"],"tip":""}],"overallFeedback":[{"from":0,"to":100}],"solvedLabel":"Progress:","scoreLabel":"Wrong answers:","resultLabel":"Your result","labelCorrect":"Correct.","labelIncorrect":"Incorrect! Please try again.","alternativeIncorrectLabel":"Incorrect","labelCorrectAnswers":"Correct answers.","tipButtonLabel":"Show tip","scoreBarLabel":"You got :num out of :total points","progressText":"Progress :num of :total"},"subContentId":"3459bb32-7f15-440b-ad51-e9d9f12add2a","metadata":{"contentType":"Summary","license":"U","title":"How to describe \\(\\vec{u} + t\\vec{v}\\) geometrically?"}},"pause":true,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""}},"label":""},{"x":47.797356828193834,"y":46.08610567514677,"width":10,"height":10,"duration":{"from":137.835,"to":147.835},"libraryTitle":"Fill in the Blanks","action":{"library":"H5P.Blanks 1.14","params":{"media":{"disableImageZooming":false},"text":"Fill in the missing words","overallFeedback":[{"from":0,"to":100}],"showSolutions":"Show solution","tryAgain":"Retry","checkAnswer":"Check","notFilledOut":"Please fill in all blanks to view solution","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":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"You got :num out of :total points","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"questions":["

Let the magnitude of \\(\\vec{v} = (2,3)\\) be d. Then \\(d^2\\) = *13*.<\/p>\n"]},"subContentId":"8404a49b-76ea-4bce-aa31-05c59c8990a9","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"magnitude of a vector"}},"pause":true,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""},{"x":47.797356828193834,"y":46.08610567514677,"width":10,"height":10,"duration":{"from":155.294,"to":165.294},"libraryTitle":"True\/False Question","action":{"library":"H5P.TrueFalse 1.8","params":{"media":{"disableImageZooming":false},"correct":"false","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"feedbackOnWrong":"When t is negative, \\(t |\\vec{v}|\\) would be negative so we need the absolute value sign."},"l10n":{"trueText":"True","falseText":"False","score":"You got @score of @total points","checkAnswer":"Check","showSolutionButton":"Show solution","tryAgain":"Retry","wrongAnswerMessage":"Wrong answer","correctAnswerMessage":"Correct answer","scoreBarLabel":"You got :num out of :total points"},"confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"question":"

For any given vector \\(\\vec{v}\\), we always have \\( |t\\vec{v}| = t|\\vec{v}|.\\) <\/p>\n"},"subContentId":"0e27158b-f859-4a08-b9fe-8e880d6374c0","metadata":{"contentType":"True\/False Question","license":"U","title":"scalar multiple of a vector"}},"pause":false,"displayType":"button","buttonOnMobile":false,"adaptivity":{"correct":{"allowOptOut":false,"message":""},"wrong":{"allowOptOut":false,"message":""},"requireCompletion":false},"label":""}],"endscreens":[{"time":228,"label":"3:48 Submit screen"}]},"summary":{"task":{"library":"H5P.Summary 1.10","params":{"intro":"Choose the correct statement.","summaries":[{"subContentId":"816e6e2a-aa0d-4146-9785-78f5552a5ee5","tip":""}],"overallFeedback":[{"from":0,"to":100}],"solvedLabel":"Progress:","scoreLabel":"Wrong answers:","resultLabel":"Your result","labelCorrect":"Correct.","labelIncorrect":"Incorrect! Please try again.","alternativeIncorrectLabel":"Incorrect","labelCorrectAnswers":"Correct answers.","tipButtonLabel":"Show tip","scoreBarLabel":"You got :num out of :total points","progressText":"Progress :num of :total"},"subContentId":"5bc06d4e-14c0-48d5-b348-b44d9f780940","metadata":{"contentType":"Summary","license":"U","title":"Untitled Summary"}},"displayAt":3}},"override":{"autoplay":false,"loop":false,"showBookmarksmenuOnLoad":false,"showRewind10":false,"deactivateSound":false,"preventSkippingMode":"none"},"l10n":{"interaction":"Interaction","play":"Play","pause":"Pause","mute":"Mute","unmute":"Unmute","quality":"Video Quality","captions":"Captions","close":"Close","fullscreen":"Fullscreen","exitFullscreen":"Exit Fullscreen","summary":"Open summary dialog","bookmarks":"Bookmarks","endscreen":"Submit screen","defaultAdaptivitySeekLabel":"Continue","continueWithVideo":"Continue with video","playbackRate":"Playback Rate","rewind10":"Rewind 10 Seconds","navDisabled":"Navigation is disabled","sndDisabled":"Sound is disabled","requiresCompletionWarning":"You need to answer all the questions correctly before continuing.","back":"Back","hours":"Hours","minutes":"Minutes","seconds":"Seconds","currentTime":"Current time:","totalTime":"Total time:","singleInteractionAnnouncement":"Interaction appeared:","multipleInteractionsAnnouncement":"Multiple interactions appeared.","videoPausedAnnouncement":"Video is paused","content":"Content","answered":"@answered answered","endcardTitle":"@answered Question(s) answered","endcardInformation":"You have answered @answered questions, click below to submit your answers.","endcardInformationNoAnswers":"You have not answered any questions.","endcardInformationMustHaveAnswer":"You have to answer at least one question before you can submit your answers.","endcardSubmitButton":"Submit Answers","endcardSubmitMessage":"Your answers have been submitted!","endcardTableRowAnswered":"Answered questions","endcardTableRowScore":"Score","endcardAnsweredScore":"answered","endCardTableRowSummaryWithScore":"You got @score out of @total points for the @question that appeared after @minutes minutes and @seconds seconds.","endCardTableRowSummaryWithoutScore":"You have answered the @question that appeared after @minutes minutes and @seconds seconds."}}

vectors

Description

Xinli Wang