## Dot Products

### My complicated derivation

Preface There’s a simpler derivation using the geometric defintion linearity from the definition orthogonality of the canonical basic vectors $\vec{i}$, $\vec{j}$ and $\vec{k}$. If I had read that, I wouldn’t have type this document in LaTeX. The following content was transcribed from a PDF file that I made three days ago. Content Recall: $\sum_{i=m}^{n} a_{i}=a_{m}+a_{m+1}+a_{m+2}+\cdots +a_{n-1}+a_{n},$ where $m$, $n$ are integers. Example: $\sum_{i=3}^6 i^2 = 3^2 + 4^2 + 5^2 + 6^2 = 86$ [Read More]