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This perspective gives a very elegant explanation of why the traditional computation of a dot product corresponds to its geometric interpretation.\n\nMinor error at 1:44, the third line of the matrix should read \"v1 * w2 - w1 * v2\"\n\n*Note, in all the computations here, I list the coordinates of the vectors as columns of a matrix, but many textbooks put them in the rows of a matrix instead.  It makes no difference for the result since the determinant is unchanged after a transpose, but given how I've framed most of this series I think it is more intuitive to go with a column-centric approach.\n\nFull series: http://3b1b.co/eola\n\nFuture series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.\nhttp://3b1b.co/support\n\nThanks to these viewers for their contributions to translations\nHebrew: Omer Tuchfeld\nVietnamese: @ngvutuan2811\n\n------------------\n\n3blue1brown is a channel about animating math, in all senses of the word animate.  And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).\n\nIf you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ\n\nVarious social media stuffs:\nWebsite: https://www.3blue1brown.com\nTwitter: https://twitter.com/3Blue1Brown\nPatreon: https://patreon.com/3blue1brown\nFacebook: https://www.facebook.com/3blue1brown\nReddit: https://www.reddit.com/r/3Blue1Brown", "channel_id": "UCYO_jab_esuFRV4b17AJtAw", "channel_url": "https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw", "duration": 790, "view_count": 1619897, "age_limit": 0, "webpage_url": "https://www.youtube.com/watch?v=BaM7OCEm3G0", "categories": ["Education"], "tags": [], "playable_in_embed": true, "live_status": "not_live", "media_type": "video", "_format_sort_fields": ["quality", "res", "fps", "hdr:12", "source", "vcodec", "channels", "acodec", "lang", "proto"], 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