This page covers the concepts of dot product, vector length, distance, and orthogonality within vector spaces. It defines the dot product mathematically in \(\mathbb{R}^n\) and explains properties lik...This page covers the concepts of dot product, vector length, distance, and orthogonality within vector spaces. It defines the dot product mathematically in \(\mathbb{R}^n\) and explains properties like commutativity and distributivity. Length is derived from the dot product, and the distance between points is defined as the length of the connecting vector. Unit vectors are introduced, and orthogonality is defined as having a dot product of zero.
