[tex]\begin{gathered} v=3i+j\rightarrow v=(3,1) \\ w=i+3j\rightarrow w=(1,3) \\ For\text{ v}\cdot w \\ v\cdot w=(3\cdot1)+(1\cdot3) \\ v\cdot w=3+3 \\ v\cdot w=6 \\ \text{For v}\cdot v \\ v\cdot v=(3\cdot3)+(1\cdot1) \\ v\cdot v=9+1 \\ v\cdot v=10 \end{gathered}[/tex]
