[78] 外積ベクトル 解説 諸性質（なぜ大きさを面積で取るのか、体積と行列式、スカラー三重積・ベクトル三重積など）

Contents: Thanks for watching. This video is a further content of cross product of vectors for those who have already watched and learned the previous videos about it. I mainly explained about scalar triple product and vector triple product, and I unexpectedly talked about quaternion and maths' history around Hamilton. 動画の内容：外積ベクトルの解説動画の続きです。定義と初歩的性質、演習の後は深掘りです。意外に面白い性質と等式がありますのでご覧ください。例えばスカラー三重積とベクトル三重積などですね。とはいえ統一的に語るためには線型代数や四元数の枠組みの中で語る方が良いので結構厳しいことではありますがとりあえずやってみました。また、ハミルトンと四元数についての数学史と雑学も最後の方に駄弁っています。お楽しみに。 -------------------------------------------------------------------------------- 主に数学に関することを動画にしています。みんなで面白いことをあーだこーだ言えたらいいなと。 動画に関するアドバイス（声量・ライト・ペン・板書など）や動画にしてほしいことなど何でも受け付けております。むしろください。 連絡等はこちらに→maths.toshi@gmail.com Thanks a ton for visiting here and reading this. Please subscribe this channel and give this video a like if you like it. I usually make videos about mathematics, but any kinds of topics which I find interesting and attractive. All I want to do is just discuss and talk about them, and communicate with people who are into maths, after all. I am afraid to say that I basically speak in Japanese in my videos; however, I am going to try and write things down in the way everyone can comprehend what they are, not without mathematics literacy at least :-). I would appreciate if you gave me any kind of advice ranging from the topics you would like me to bring about to the volume, my handwriting, and the lighting in my videos. Please do not hesitate to leave any comments for this channel growth, and help me to enrich this channel.