For anyone who wants to understand the cross product more deeply, this video shows how it relates to a certain linear transformation via duality. This perspective gives a very elegant explanation of why the traditional computation of a dot product corresponds to its geometric interpretation.
*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: 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: goo.gl/WmnCQZ
This introduces the "Essence of Linear Algebra" series, aimed at animating the geometric intuitions underlying many of the topics taught in a standard linear algebra course.
This course is perfect for any high school student interested in exploring the world of Linear Algebra, which any math and engineering student will face in their college years. Furthermore, this course is perfect for any university and adult learner who wants an intuitive, original, and entertaining explanation of simple and complex Linear Algebra concepts.