2 12 The inner product and orthogonality

This video introduces secondary school students, who may have not yet been exposed to vectors, the relationship between the inner product and the angle between two 2-dimensional vectors, with an emphasis on using this to determine orthogonality. It gives some sample calculations, and makes a few observations.

This is my personal favorite, because while other topics have been covered in a way that I consider unique and interesting, this is a derivation of the inner product from definitions of secondary school, and the inner product falls out of the derivation. Every source online I have seen more-or-less assumes that or defines that the inner product equals ||u|| ||v|| cos(theta).

This is part of the series "A primer on vectors". A pdf is available on the NE 112 course web site.