Space Inner Product

Why

We want to measure angles in space.¹

Definition

The space inner product (or dot product, scalar product) of two real vectors $x, y \in \R ^3$ is

\[ x_1y_1 + x_2y_2 + x_3y_3 \]

Notation

We denote the inner product of $x$ and $y$ by $\ip{x,y}$.

1. Future editions will include pictures. ↩︎