Dot Product

Given two vectors $\vec{\text{u}}=⟨\text{u}1,\text{u}2⟩$ and $\vec { \text{v} }= ⟨\text{v}1, \text{v}2⟩$ , the dot product (also called inner product or scalar product) is:

$\vec{\text{u}}·\vec{\text{v}}=\text{u}_1\text{v}_1+\text{u}_2\text{v}_2$ 

Example: If $\vec { \text{u} }= ⟨–2, 7⟩$ and $\vec { \text{v} }= ⟨3, 4⟩$ , then $\vec { \text{u} } · \vec{\text{v}}= –2(3) + 7(4) = 22$.

Another formula for the dot product is:

$\vec { \text{u} } \cdot \vec { \text{v} } = \| \text{u} \| \| \text{v} \| \cos ( \theta )$, where θ is the angle between $\vec { \text{u} }$ and $\vec { \text{v} }$