Math — Vector Geometry

|\mathbf{a}| = \sqrt{a_1^2 + a_2^2 + a_3^2}

\mathbf{a}\cdot\mathbf{b} = a_1b_1 + a_2b_2 + a_3b_3

\hat{\mathbf{a}} = \frac{\mathbf{a}}{|\mathbf{a}|}

\mathbf{a} \parallel \mathbf{b} \Leftrightarrow \mathbf{a} = \lambda\mathbf{b}