Worked Example

Problem:
Find $\vec{A} \cdot \vec{B}$ for:

$$ \vec{A} = (1,2,3), \quad \vec{B} = (4,5,6) $$

Solution

$$ \vec{A} \cdot \vec{B} = 1\cdot4 + 2\cdot5 + 3\cdot6 = 32 $$