This covers the main geometric intuition behind the 2d and 3d cross products. *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. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb ------------------ 3blue1brown 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). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown

I imagine many viewers are already familiar with vectors in some context, so this video is intended both as a quick review of vector terminology, as well as a chance to make sure we're all on the same page about how specifically to think about vectors in the context of linear algebra. Watch the full "Essence of linear algebra" playlist here: https://goo.gl/R1kBdb ------------------ 3blue1brown 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). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown

The Bitcoin protocol and blockchains explained from the viewpoint of stumbling into inventing your own cryptocurrency. Protocol Labs: https://protocol.ai/ Interested in contributing? https://protocol.ai/join/ Special thanks to the following patrons: http://3b1b.co/btc-thanks Some people have asked if this channel accepts contributions in cryptocurrency form as an alternative to Patreon. As you might guess, the answer is yes :). Here are the relevant addresses: ETH: 0x88Fd7a2e9e0E616a5610B8BE5d5090DC6Bd55c25 BTC: 1DV4dhXEVhGELmDnRppADyMcyZgGHnCNJ LTC: LNPY2HEWv8igGckwKrYPbh9yD28XH3sm32 Supplement video: https://youtu.be/S9JGmA5_unY Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/heartbeat Here are a few other resources I'd recommend: Original Bitcoin paper: https://bitcoin.org/bitcoin.pdf Block explorer: https://blockexplorer.com/ Blog post by Michael Nielsen: https://goo.gl/BW1RV3 (This is particularly good for understanding the details of what transactions look like, which is something this video did not cover) Video by CuriousInventor: https://youtu.be/Lx9zgZCMqXE Video by Anders Brownworth: https://youtu.be/_160oMzblY8 Ethereum white paper: https://goo.gl/XXZddT ------------------ 3blue1brown 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 on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown

Trapped in the hotel room, Nic & Gareth learn that they would have been off on a hot-air balloon ride had they been on holiday. Can they make do? And who is Nic's new friend? Enter for your chance to win a dream holiday for two worth R60k by tweeting https://twitter.com/efferfluC using the hashtag #projecttrapped and give them suggestions on how to pass the time while they're trapped in the hotel room! Go to http://www.projecttrapped.co.za to find out more. EPISODE 1: https://www.youtube.com/watch?v=-4WdIPx47Ls&list=UUmZhiZq7M7d73Kbey4yna_Q EPISODE 3: http://youtu.be/irbJKRU3GDM EPISODE 4: http://youtu.be/UtfecyOWZX0 Don't miss out on a single episode of Project Trapped - hit SUBSCRIBE now! ============== Video Credits: ============== A Chasing Migada Production Director - Quinton Lavery Producers - Chasing Migada Productions and Derick Watts & The Sunday Blues Writers - Nicholas Smal & Gareth Allison Director of Photography - Darren Wertheim Production Designer - Kaley Elizabeth Claire Sound Recordist - Greg Alberts Editor - Joshua Borril Sound Mixer - Nic Turton Camera & Lighting Assistant - Roscoe Vercueil Catering - Kerry Farrelly Written by & starring Nic Smal and Gareth Allison Special Thanks: Winchester Mansions Hotel, Media Film Service, Flash Photo Hire, Saatchi & Saatchi Synergize.