Answer
$\vec{u}\cdot(\vec{v}+\vec{w})=9$
Work Step by Step
$\vec{u}=2\vec{i}+\vec{j}$ $,$ $\vec{v}=\vec{i}-3\vec{j}$ and $\vec{w}=3\vec{i}+4\vec{j}$
$\vec{u}\cdot(\vec{v}+\vec{w})$
Find $\vec{v}+\vec{w}$:
$\vec{v}+\vec{w}=(1+3)\vec{i}+(-3+4)\vec{j}=4\vec{i}+\vec{j}$
Find $\vec{u}\cdot(\vec{v}+\vec{w})$ by multiplying corresponding components and adding:
$\vec{u}\cdot(\vec{v}+\vec{w})=(2)(4)+(1)(1)=8+1=9$
