06外积Cross product简介

>> DOWNLOAD LINK 🎞️ #1 <<

>> DOWNLOAD LINK 🎞️ #2 <<

>> COPY / PASTE LINK PLEASE 🎵 MP3 <<

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=x_o-JqRMOKs

Shareyoucan免费在线学习课程","styleRuns":[{"startIndex":0,"length":19,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":19,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CKsBELsvGAIiEwip6ru7gPCLAxVqdXoFHYUgCXc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC3hfby1KcVJNT0tzGAYyJSIRIgt4X28tSnFSTU9LczAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CKsBELsvGAIiEwip6ru7gPCLAxVqdXoFHYUgCXc=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CKoBELovIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"WaqQl_TzsWw","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/WaqQl_TzsWw/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCAlhhJbpgZKQHzfNasoVmLbRu05Q","width":168,"height":94},{"url":"https://i.ytimg.com/vi/WaqQl_TzsWw/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLAIUIylyyt5URSEtoZ63QRZ_3clPQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"07外积和右手坐标系Right Handed Coordinate System by PengTitus 9,965 views 15 years ago 5 minutes, 15 seconds"}},"simpleText":"07外积和右手坐标系Right Handed Coordinate System"},"longBylineText":{"runs":[{"text":"PengTitus","navigationEndpoint":{"clickTrackingParams":"CKQBEKQwGAAiEwip6ru7gPCLAxVqdXoFHYUgCXcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PengTitus","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCci8XOD1wSL4U91IzLqC3fQ","canonicalBaseUrl":"/@PengTitus"}}}]},"publishedTimeText":{"simpleText":"15 years ago"},"viewCountText":{"simpleText":"9,965 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"5 minutes, 15 seconds"}},"simpleText":"5:15"},"navigationEndpoint":{"clickTrackingParams":"CKQBEKQwGAAiEwip6ru7gPCLAxVqdXoFHYUgCXcyB3JlbGF0ZWRIq_GwourEj_3HAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=WaqQl_TzsWw","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"WaqQl_TzsWw","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=59aa9097f4f3b16c ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1686250 mt=1741076467 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"PengTitus","navigationEndpoint":{"clickTrackingParams":"CKQBEKQwGAAiEwip6ru7gPCLAxVqdXoFHYUgCXcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PengTitus","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCci8XOD1wSL4U91IzLqC3fQ","canonicalBaseUrl":"/@PengTitus"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lzrnGJnE64ehtlZQQ5iLqWUOnz2XbRwvA-o-Qt0sQdqA=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CKQBEKQwGAAiEwip6ru7gPCLAxVqdXoFHYUgCXdA7OLOp_-SpNVZ","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"9.9K views"}},"simpleText":"9.9K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CKgBEP6YBBgFIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKgBEP6YBBgFIhMIqeq7u4DwiwMVanV6BR2FIAl3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"WaqQl_TzsWw","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKgBEP6YBBgFIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["WaqQl_TzsWw"],"params":"CAQ%3D"}},"videoIds":["WaqQl_TzsWw"]}},{"clickTrackingParams":"CKgBEP6YBBgFIhMIqeq7u4DwiwMVanV6BR2FIAl3","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CKkBELlqIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},"popupType":"TOAST"}}]}},"trackingParams":"CKgBEP6YBBgFIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CKQBEKQwGAAiEwip6ru7gPCLAxVqdXoFHYUgCXc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtXYXFRbF9UenNXdw%3D%3D","commands":[{"clickTrackingParams":"CKQBEKQwGAAiEwip6ru7gPCLAxVqdXoFHYUgCXc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKcBEI5iIhMIqeq7u4DwiwMVanV6BR2FIAl3","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CKQBEKQwGAAiEwip6ru7gPCLAxVqdXoFHYUgCXc=","hasSeparator":true}}],"trackingParams":"CKQBEKQwGAAiEwip6ru7gPCLAxVqdXoFHYUgCXc=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"5 minutes, 15 seconds"}},"simpleText":"5:15"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKYBEPnnAxgBIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"WaqQl_TzsWw","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKYBEPnnAxgBIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"WaqQl_TzsWw"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKYBEPnnAxgBIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKUBEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKUBEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"WaqQl_TzsWw","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKUBEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["WaqQl_TzsWw"],"params":"CAQ%3D"}},"videoIds":["WaqQl_TzsWw"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKUBEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"07外积和右手坐标系Right Handed Coordinate System - 5 minutes, 15 seconds - Go to channel - PengTitus - 9.9K views - 15 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"bImKWOgFyH0","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/bImKWOgFyH0/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-BIAC4AOKAgwIABABGF4gWyhlMA8= rs=AOn4CLDkqLy94K5VlfLfgg9rcLgrLrlDVg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/bImKWOgFyH0/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gSAAuADigIMCAAQARheIFsoZTAP rs=AOn4CLBRt5R76sY04K5wkKecDnzr0boDOw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"01向量概论 by PengTitus 15,020 views 15 years ago 9 minutes, 44 seconds"}},"simpleText":"01向量概论"},"longBylineText":{"runs":[{"text":"PengTitus","navigationEndpoint":{"clickTrackingParams":"CJ4BEKQwGAEiEwip6ru7gPCLAxVqdXoFHYUgCXcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PengTitus","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCci8XOD1wSL4U91IzLqC3fQ","canonicalBaseUrl":"/@PengTitus"}}}]},"publishedTimeText":{"simpleText":"15 years ago"},"viewCountText":{"simpleText":"15,020 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"9 minutes, 44 seconds"}},"simpleText":"9:44"},"navigationEndpoint":{"clickTrackingParams":"CJ4BEKQwGAEiEwip6ru7gPCLAxVqdXoFHYUgCXcyB3JlbGF0ZWRIq_GwourEj_3HAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=bImKWOgFyH0","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"bImKWOgFyH0","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=6c898a58e805c87d ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1273750 mt=1741076467 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"PengTitus","navigationEndpoint":{"clickTrackingParams":"CJ4BEKQwGAEiEwip6ru7gPCLAxVqdXoFHYUgCXcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PengTitus","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCci8XOD1wSL4U91IzLqC3fQ","canonicalBaseUrl":"/@PengTitus"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lzrnGJnE64ehtlZQQ5iLqWUOnz2XbRwvA-o-Qt0sQdqA=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CJ4BEKQwGAEiEwip6ru7gPCLAxVqdXoFHYUgCXdA_ZCXwI7L4sRs","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"15K views"}},"simpleText":"15K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CKIBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKIBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"bImKWOgFyH0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKIBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["bImKWOgFyH0"],"params":"CAQ%3D"}},"videoIds":["bImKWOgFyH0"]}},{"clickTrackingParams":"CKIBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CKMBELlqIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},"popupType":"TOAST"}}]}},"trackingParams":"CKIBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJ4BEKQwGAEiEwip6ru7gPCLAxVqdXoFHYUgCXc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtiSW1LV09nRnlIMA%3D%3D","commands":[{"clickTrackingParams":"CJ4BEKQwGAEiEwip6ru7gPCLAxVqdXoFHYUgCXc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKEBEI5iIhMIqeq7u4DwiwMVanV6BR2FIAl3","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJ4BEKQwGAEiEwip6ru7gPCLAxVqdXoFHYUgCXc=","hasSeparator":true}}],"trackingParams":"CJ4BEKQwGAEiEwip6ru7gPCLAxVqdXoFHYUgCXc=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"9 minutes, 44 seconds"}},"simpleText":"9:44"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKABEPnnAxgBIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"bImKWOgFyH0","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKABEPnnAxgBIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"bImKWOgFyH0"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKABEPnnAxgBIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJ8BEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJ8BEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"bImKWOgFyH0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJ8BEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["bImKWOgFyH0"],"params":"CAQ%3D"}},"videoIds":["bImKWOgFyH0"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJ8BEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"01向量概论 - 9 minutes, 44 seconds - Go to channel - PengTitus - 15K views - 15 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/bImKWOgFyH0/mqdefault_6s.webp?du=3000 sqp=CMPbmr4G rs=AOn4CLBsKrOXE64BRWRure9f-OsPqzciYQ","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"Kti2mNKDOTw","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/Kti2mNKDOTw/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBfsknv_5dtcGpQyaxYtvoEhrznJA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/Kti2mNKDOTw/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDDp8Tq10vBL8HwzMsddDmtVcOSXA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"05内积Dot product简介 by PengTitus 20,250 views 15 years ago 8 minutes, 9 seconds"}},"simpleText":"05内积Dot product简介"},"longBylineText":{"runs":[{"text":"PengTitus","navigationEndpoint":{"clickTrackingParams":"CJgBEKQwGAIiEwip6ru7gPCLAxVqdXoFHYUgCXcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PengTitus","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCci8XOD1wSL4U91IzLqC3fQ","canonicalBaseUrl":"/@PengTitus"}}}]},"publishedTimeText":{"simpleText":"15 years ago"},"viewCountText":{"simpleText":"20,250 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"8 minutes, 9 seconds"}},"simpleText":"8:09"},"navigationEndpoint":{"clickTrackingParams":"CJgBEKQwGAIiEwip6ru7gPCLAxVqdXoFHYUgCXcyB3JlbGF0ZWRIq_GwourEj_3HAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=Kti2mNKDOTw","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"Kti2mNKDOTw","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr2---sn-nvm-cxb6.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=2ad8b698d283393c ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1572500 mt=1741076467 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"PengTitus","navigationEndpoint":{"clickTrackingParams":"CJgBEKQwGAIiEwip6ru7gPCLAxVqdXoFHYUgCXcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PengTitus","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCci8XOD1wSL4U91IzLqC3fQ","canonicalBaseUrl":"/@PengTitus"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lzrnGJnE64ehtlZQQ5iLqWUOnz2XbRwvA-o-Qt0sQdqA=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CJgBEKQwGAIiEwip6ru7gPCLAxVqdXoFHYUgCXdAvPKMlI3Trewq","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"20K views"}},"simpleText":"20K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJwBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJwBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"Kti2mNKDOTw","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJwBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["Kti2mNKDOTw"],"params":"CAQ%3D"}},"videoIds":["Kti2mNKDOTw"]}},{"clickTrackingParams":"CJwBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJ0BELlqIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},"popupType":"TOAST"}}]}},"trackingParams":"CJwBEP6YBBgGIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJgBEKQwGAIiEwip6ru7gPCLAxVqdXoFHYUgCXc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtLdGkybU5LRE9Udw%3D%3D","commands":[{"clickTrackingParams":"CJgBEKQwGAIiEwip6ru7gPCLAxVqdXoFHYUgCXc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CJsBEI5iIhMIqeq7u4DwiwMVanV6BR2FIAl3","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJgBEKQwGAIiEwip6ru7gPCLAxVqdXoFHYUgCXc=","hasSeparator":true}}],"trackingParams":"CJgBEKQwGAIiEwip6ru7gPCLAxVqdXoFHYUgCXc=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"8 minutes, 9 seconds"}},"simpleText":"8:09"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJoBEPnnAxgBIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"Kti2mNKDOTw","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CJoBEPnnAxgBIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"Kti2mNKDOTw"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJoBEPnnAxgBIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJkBEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJkBEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"Kti2mNKDOTw","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJkBEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["Kti2mNKDOTw"],"params":"CAQ%3D"}},"videoIds":["Kti2mNKDOTw"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJkBEMfsBBgCIhMIqeq7u4DwiwMVanV6BR2FIAl3"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"05内积Dot product简介 - 8 minutes, 9 seconds - Go to channel - PengTitus - 20K views - 15 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/Kti2mNKDOTw/mqdefault_6s.webp?du=3000 sqp=CIDWmr4G rs=AOn4CLAq4GTtw7liIlpTeUPo0QgkyphGHw","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/WIejVc3u0F4/hqdefault.jpg?sqp=-oaymwEwCKgBEF5IWvKriqkDIwgBFQAAiEIYAfABAfgB_gSAAuADigIMCAAQARhlIEMoQTAP rs=AOn4CLA-2cH7zqnzaBosJUUeIUZTI_JJeg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/WIejVc3u0F4/hqdefault.jpg?sqp=-oaymwExCNACELwBSFryq4qpAyMIARUAAIhCGAHwAQH4Af4EgALgA4oCDAgAEAEYZSBDKEEwDw== rs=AOn4CLCL2tCcF-U_ajrjuf_b_ZsuuvBmtw","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"29 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3350816,"darkTheme":3350816}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4139560,"darkTheme":4139560}}},"stackColor":{"lightTheme":10055019,"darkTheme":9664630}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"高中数学向量线上影音教学PengTitus版"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"PengTitus

#############################