5.7 Cosine Formula for Inner Product

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 5.1 Inner Product Between Vectors

Properties: N/A
Sufficiencies: 5.6 Law of Cosines
Questions: N/A

Cosine Formula for Inner Product

Let $n \in N$ be a positive integer and let 3.1 Column Vector $\vec{x}, \vec{y} \in R^{n}$ . Then, the dot product satisfies

\vec{x} \cdot \vec{y} = | | \vec{x} | | | | \vec{y} | | \cos θ

where $θ$ is the angle between the vectors $\vec{x}$ and $\vec{y}$ .

\begin{proof}
![[Lesson 5 Inner Products & Vector Norms.pdf]]
\end{proof}