A unit vector in direction of $\vec{a}$ is denoted by $\hat{\vec{a}}$
+Also, unit vector of $\vec{a}$ can be defined by $\vec{a} \cdot {|\vec{a}|}$
+
+## Scalar products / dot products
+
+If $\vec{a} = a_i \vec{i} + a_2 \vec{j}$ and $\vec{b} = b_i \vec{i} + b_2 \vec{j}$, the dot product is:
+$$\vec{a} \cdot \vec{b} = a_1 b_1 + a_2 b_2$$
+
+Produces a real number, not a vector.
+
+$$\vec{a} \cdot \vec{a} = |\vec{a}|^2$$
+
+## Geometric scalar products
+
+$$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta$$
+
+where $0 \le \theta \le \pi$
+
+## Perpendicular vectors
+
+If $\vec{a} \cdot \vec{b} = 0$, then $\vec{a} \perp \vec{b}$ (since $\cos 90 = 0$)
+
+## Finding angle between vectors
+
+$$\cos \theta = {{\vec{a} \cdot \vec{b}} \over {|\vec{a}| |\vec{b}|}} = {{a_1 b_1 + a_2 b_2} \over {|\vec{a}| |\vec{b}|}}$$