- Two vectors $\boldsymbol{a}$ and $\boldsymbol{b}$ are perpendicular if $\boldsymbol{a} \cdot \boldsymbol{b}=0$
- $\boldsymbol{a} \cdot \boldsymbol{a} = |\boldsymbol{a}|^2$
+## Linear dependence
+Vectors $\vec{a}, \vec{b}, \vec{c}$ are linearly dependent if they are non-parallel and:
+$$k\vec{a}+l\vec{b}+m\vec{c} = 0$$
+$$\therefore \vec{c} = m\vec{a} + n\vec{b} \quad \text{(simultaneous)}$$
+$\vec{a}, \vec{b},$ and $\vec{c}$ are linearly independent if no vector in the set is expressible as a linear combination of other vectors in set, or if they are parallel.
+
+Vector $\vec{w}$ is a linear combination of vectors $\vec{v_1}, \vec{v_2}, \vec{v_3}$